STATICS -02-ASSIGNMENT

1. The resultant of two forces 3P and 2P is R, if the first force is doubled, the resultant is also doubled. The angle between the forces is (a) (b) (c) (d) 2. The resultant of two forces and is of magnitude P. If the force is doubled, remaining unaltered, the new resultant will be (a) Along (b) Along (c) At to (d) At right angle to 3. If the resultant of two forces 2P and is , then the angle between them will be (a) (b) (c) (d) 4. The maximum resultant of two forces is P and the minimum resultant is , the two forces are at right angles, the resultant is (a) (b) (c) (d) 5. Two equal forces act at a point. If the square of the magnitude of their resultant is three times the product of their magnitudes, the angle between the forces is (a) (b) (c) (d) 6. A force is resolved into components P and Q equally inclined to it. Then (a) (b) (c) (d) None of these 7. If the square of the resultant of two equal forces is equal to times their product, then the angle between the forces is (a) (b) (c) (d) 8. The resultant of two equal forces is equal to either of these forces. The angle between them is (a) (b) (c) (d) 9. When two equal forces are inclined at an angle , their resultant is twice as great as when they act at an angle , then (a) (b) (c) (d) 10. Two forces of 13 N and N act on a particle at an angle and are equal to a resultant force of 14N, the angle between the forces is (a) (b) (c) (d) 11. If two forces and make an angle with each other and their resultant makes an angle with the bisector of the angle between the two forces, then is equal to (a) (b) (c) (d) 12. A force F is resolved into two components P and Q. If P be at right angles to F and has the same magnitude as that of F, then the magnitude of Q is (a) (b) (c) (d) 13. The direction of three forces 1N, 2N and 3N acting at a point are parallel to the sides of an equilateral triangle taken in order, The magnitude of their resultant is [Roorkee Screening 1993] (a) (b) 3N (c) (d) 14. Forces of magnitudes 5, 10, 15 and 20 Newton act on a particle in the directions of North, South, East and West respectively. The magnitude of their resultant is (a) (b) (c) (d) 15. Forces of magnitudes and act at a point parallel to the sides of an equilateral triangle taken in order. The resultant of these forces, is (a) (b) (c) (d) 16. Two forces acting in opposite directions on a particle have a resultant of 34 Newton; if they acted at right angles to one another, their resultant would have a magnitude of 50 Newton. The magnitude of the forces are (a) 48, 14 (b) 42, 8 (c) 40, 6 (d) 36, 2 17. Three forces of magnitude 30, 60 and P acting at a point are in equilibrium. If the angle between the first two is , the value of P is (a) (b) (c) (d) 18. The resultant of two forces P and Q acting at an angle is equal to ; when they act at an angle , the resultant is ; then = (a) (b) (c) (d) 19. If forces of magnitude P, Q and R act at a point parallel to the sides BC, CA and AB respectively of a , then the magnitude of their resultant is (a) (b) (c) (d) None of these 20. Two forces of magnitudes and Newton are acting at an angle of . If their resultant is a force of 2 Newton perpendicular to the line of action of the second force, then (a) (b) (c) (d) 21. Let R be the resultant of P and Q and if , then the angle between P and R is (a) (b) (c) (d) 22. The resultant of two forces P and Q is at right angles to P, the resultant of P and acting at the same angle is at right angles to . Then, (a) are in GP (b) are in GP (c) are in GP (d) None of these 23. The resultant R of two forces P and Q act at right angles to P. Then the angle between the forces is (a) (b) (c) (d) 24. The sum of the two forces is 18 and their resultant perpendicular to the lesser of the forces is 12, then the lesser force is (a) 5 (b) 3 (c) 7 (d) 15 25. The magnitudes of two forces are 3, 5 and the direction of the resultant is at right angles to that of the smaller force. The ratio of the magnitude of the larger force and of the resultant is (a) 5 : 3 (b) 5 : 4 (c) 4 : 5 (d) 4 : 3 26. If the resultant of two forces P and Q is and makes an angle 30o with the direction of P, then (a) (b) (c) (d) None of these 27. The resolved part of a force of 16 Newton in a direction is Newton. The inclination of the direction of the resolved part with the direction of the force is (a) (b) (c) (d) 28. Let P, 2P and 3P be the forces acting along AB, BC, CA of an equilateral . Suppose R is the magnitude of their resultant and the angle made by the resultant with the side BC, then (a) (b) (c) (d) 29. When a particle be kept at rest under the action of the following forces (a) (b) (c) (d) 30. In a triangle ABC three forces of magnitudes and are acting along the sides AB, AC and CB respectively. If the resultant meets AC at , then the ratio DC : AD will be equal to (a) 1 : 1 (b) 1 : 2 (c) 1: 3 (d) 1: 4 31. ABC is a triangle. Forces P, Q, R act along the lines OA, OB and OC and are in equilibrium. If O is incentre of , then (a) (b) (c) (d) None of these 32. If the forces of 12, 5 and 13 units weight balance at a point, two of them are inclined at (a) (b) (c) (d) 33. Forces of 1, 2 units act along the lines and . The equation of the line of action of the resultant is (a) (b) (c) (d) 34. If N is resolved in two components such that first is twice of other, the components are (a) (b) (c) (d) None of these 35. O is the circumcentre of . If the forces P, Q and R acting along OA, OB, and OC are in equilibrium then P : Q : R is (a) (b) (c) (d) 36. Three forces P, Q and R acting on a particle are in equilibrium. If the angle between P and Q is double the angle between P and R, then P is equal to (a) (b) (c) (d) 37. A smooth sphere is supported in contact with a smooth vertical wall by a string fastened to a point on its surface, the other end being attached to a point in the wall. If the length of the string is equal to the radius of the sphere, the tension of the string is (a) (b) (c) (d) None of these 38. Three forces P, Q, R are acting at a point in a plane. The angle between P, Q and Q, R are and respectively, then for equilibrium; forces P, Q, R are in the ratio (a) 1 : 2 : 3 (b) 1 : 2: 31/2 (c) 3 : 2 : 1 (d) (3)1/2:2 : 1 39. If A, B ,C are three forces in equilibrium acting at a point and if , and respectively denote the angles between A and B, B and C and C and A, then the forces are in proportion of (a) (b) (c) (d) 40. The resultant of two forces P and Q is R. If Q is doubled, R is doubled and if Q is reversed, R is again doubled. If the ratio , then x is equal to (a) 5 (b) 4 (c) 3 (d) 2 41. If the angle between two forces of equal magnitude is reduced to , then the magnitude of their resultant becomes times of the earlier one. The angle is (a) (b) (c) (d) 42. The resultant of two forces P and Q is R. If one of the forces is reversed in direction, the resultant becomes , then (a) (b) (c) (d) 43. Forces proportional to AB, BC and 2CA act along the sides of triangle ABC in order, their resultants represented in magnitude and direction is (a) CA (b) AC (c) BC (d) CB 44. The resultant of P and Q is R. If P is reversed, Q remaining the same, the resultant becomes . If R is perpendicular to , then (a) (b) (c) (d) None of these 45. is a parallelogram, a particle P is attracted towards A and C by forces proportional to PA and PC respectively and repelled from B and D by forces proportional to and . The resultant of these forces is (a) (b) (c) (d) None of these 46. A particle is acted upon by three forces P, Q and R. It cannot be in equilibrium, if = (a) (b) (c) (d) 47. Forces of 7 N, 5N and 3N acting on a particle are in equilibrium, the angle between the pair of forces 5 and 3 is (a) (b) (c) (d) 48. is a quadrilateral. Forces represented by and act on a particle. The resultant of these forces is (a) (b) (c) (d) 49. With two forces acting at a point, the maximum effect is obtained when their resultant is 4N. If they act at right angles, then their resultant is 3N. Then the forces are (a) and (b) and (c) and (d) and 50. The resultant of two forces P and Q is equal to and makes an angle of with the direction of P, then (a) 1 or 2 (b) 3 or 5 (c) 3 or 4 (d) 4 or 5 51. Two men carry a weight of 240 Newton between them by means of two ropes fixed to the weight. One rope is inclined at to the vertical and the other at . The tensions in the ropes are (a) (b) (c) (d) None of these 52. Three forces keep a particle in equilibrium. One acts towards west, another acts towards north-east and the third towards south. If the first be 5N, then other two are (a) (b) (c) (d) None of these 53. A particle is attracted to three points A, B and C by forces equal to and respectively such that their resultant is where G is the centroid of . Then (a) 1 (b) 2 (c) 3 (d) None of these 54. Three forces of magnitudes 8 Newton, 5N and 4N acting at a point are in equilibrium, then the angle between the two smaller forces is (a) (b) (c) (d) None of these 55. is an equilateral triangle. E and F are the middle- points of the sides CA and AB respectively. Forces of magnitudes 4N, PN, 2N, P N and Q N act at a point and are along the lines BC, BE, CA, CF and AB respectively. If the system is in equilibrium, then (a) (b) (c) (d) 56. The resultant of forces P and Q acting at a point including a certain angle is R, that of the forces and Q acting at the same angle is and that of and acting at the supplementary angle is . Then (a) 1 : 2 : 3 (b) (c) (d) None of these 57. The resultant of P and Q is R. If Q is doubled, R is also doubled and if Q is reversed, R is again doubled. Then is given by (a) 1 : 1: 1 (b) (c) (d) 58. The resultant of two forces acting on a particle is at right angles to one of them and its magnitude is one third of the magnitude of the other. The ratio of the larger force to the smaller is (a) (b) (c) (d) 59. is a rigid square, on which forces 2, 3 and 5 kg. wt; act along AB, AD and CA respectively. Then the magnitude of the resultant correct to one decimal place in kg. wt. is (a) 1 (b) 2 (c) 16 (d) None of these 60. A uniform rod of weight W rests with its ends in contact with two smooth planes, inclined at angles and respectively to the horizon, and intersecting in a horizontal line. The inclination of the rod to the vertical is given by (a) (b) (c) (d) All of these 61. Two forces make an angle with one another and their resultant make an angle with the bisector of the angle between them. Then (a) (b) (c) (d) None of these 62. A heavy rod 15 cm long is suspended from a fixed point by strings fastened to its ends, their lengths being 9 and 12 cm. If be the angle at which the rod is inclined to the vertical, then (a) (b) (c) (d) 63. A uniform triangular lamina whose sides are of lengths 3 cm, 4 cm and 5 cm, is suspended by a string tied at the middle point of the largest side. In equilibrium position the inclination of this side to the vertical is (a) (b) (c) (d) None of these 64. Three forces and acting along and , where I is the incentre of a , are in equilibrium . Then is (a) (b) (c) (d) 65. If two forces P and Q act on such an angle that their resultant force R is equal to force P, then if P is doubled then the angle between new resultant force and Q will be (a) (b) (c) (d) 66. What will be that force when applying along any inclined plane will stop 10 kilogram weight, it is given that force, reaction of plane and weight of body are in arithmetic series (a) 4 kilogram weight (b) 6 kilogram weight (c) 8 kilogram weight (d) 7 kilogram weight 67. A bead of weight W can slide on a smooth circular wire in a vertical plane, the bead is attached by a light thread to the highest point of the wire, and in equilibrium the thread is taut. Then the tension of the thread and the reaction of the wire on the bead, if the length of the string is equal to the radius of the wire, are (a) (b) (c) (d) None of these 68. Like parallel forces act at the vertices A, B and C of a triangle ABC and are proportional to the lengths BC, AC and AB respectively. The centre of the force is at the (a) Centroid (b) Circum- centre (c) Incentre (d) None of these 69. Three forces P, Q, R act along the sides BC, CA, AB of a taken in order, if their resultant passes through the centroid of then (a) (b) (c) (d) None of these 70. P, Q, R are the points on the sides BC, CA, AB of the triangle ABC such that . If denotes the area of the , then the forces reduce to a couple whose moment is (a) (b) (c) (d) 71. If the resultant of forces P,Q,R acting along the sides BC, CA, AB of a passes through its circumcentre, then (a) (b) (c) (d) 72. The resultant of two unlike parallel forces of magnitude P each acting at a distance of p is a (a) Force P (b) Couple of moment p.P (c) Force 2P (d) Force 73. The moment of a system of coplanar forces (not in equilibrium) about three collinear points A,B,C in the plane are then, (a) (b) (c) (d) None of these 74. A rod can turn freely about one of its ends which is fixed. At the other end a horizontal force equal to half the weight of the body is acting. In the position of equilibrium, the rod is inclined to the vertical at an angle (a) (b) (c) (d) None of these 75. The resultant of two like parallel forces P, Q passes through a point O. If the resultant also passes through O when Q and R replace P and Q respectively, then (a) are in G.P. (b) are in G.P. (c) are in G.P. (d) are in A.P. 76. Any two coplanar couples of equal moments (a) Balance each other (b) Are equivalent (c) Need not be equivalent (d) None of these 77. Two like parallel forces P and 3P act on a rigid body at points A and B respectively. If the forces are interchanged in position, the resultant will be displaced through a distance of (a) (b) (c) (d) 78. Three like parallel forces P,Q, R act at the corners A,B,C of a . If their resultant passes through the incentre of , then (a) (b) (c) (d) 79. If the sum of the resolved parts of a system of coplanar forces along two mutually perpendicular direction is zero, then the sum of the moment of the forces about a given point (a) Is zero always (b) Is positive always (c) Is negative always (d) May have any value 80. Three forces P, Q, R act along the sides BC, CA, AB of triangle ABC, taken in order. If their resultant passes through the incentre of , then (a) (b) (c) (d) None of these 81. If the resultant of two unlike parallel forces of magnitudes 10 N and 16 N act along a line at a distance of 24 cm from the line of action of the smaller force, then the distance between the lines of action of the forces is (a) 12 cm (b) 8 cm (c) 9 cm (d) 18 cm 82. If the position of the resultant of two like parallel forces P and Q is unaltered, when the positions of P and Q are interchanged, then (a) (b) (c) (d) None of these 83. Three parallel forces P,Q, R act at three points A,B, C of a rod at distances of 2m, 8m and 6m respectively from one end. If the rod be in equilibrium, then = (a) (b) (c) (d) None of these 84. The magnitude of the moment of a force about a point is (a) (b) (c) (d) 85. The resultant of two like parallel forces is 12N. The distance between the forces is 18m. If one of the force is 4N, then the distance of the resultant from the smaller force is (a) 4m (b) 8m (c) 12m (d) None of these 86. Force forming a couple are of magnitude 12N each and the arm of the couple is 8m. The force of an equivalent couple whose arm is 6m is of magnitude (a) 8N (b) 16N (c) 12N (d) 4N 87. The resultant of three equal like parallel forces acting at the vertices of a triangle act at its (a) Incentre (b) Circumcentre (c) Orthocentre (d) Centroid 88. If the force acting along the sides of a triangle, taken in order, are equivalent to a couple, then the forces are (a) Equal (b) Proportional to sides of triangle (c) In equilibrium (d) In arithmetic progression 89. If two like parallel forces of Newton and Newton have a resultant of 2 Newton, then (a) (b) (c) (d) None of these 90. Two parallel forces not having the same line of action form a couple if they are (a) Like and unlike (b) Like and equal (c) Unequal and unlike (d) Equal and unlike 91. The resultant of non parallel forces and a couple in a plane always reduces to (a) A single force (b) A couple (c) Two forces (d) None of these 92. Two like parallel forces P and 3P are 40 cm apart. If the direction of P is reversed, then their resultant shifts through a distance of (a) 30 cm (b) 40 cm (c) 50 cm (d) 60 cm 93. Let a force P be represented by the straight line AB and O is any point. Then the moment of P about O is represented in magnitude by (a) (b) (c) (d) 94. The resultant of two parallel forces P,Q acting at A and B respectively acts at C when like and at D when unlike. If P>Q, then CD = (a) (b) (c) (d) None of these 95. If the resultant of two like parallel forces of magnitudes 6N and 4N acts at a distance of 12 cm from the line of action of the smaller force, then the distance between the lines of action of the forces is (a) 18 cm (b) 24 cm (c) 20 cm (d) None of these 96. Two like parallel forces of 5N and 15 N, act on a light rod at two points A and B respectively 6m apart. The resultant force and the distance of its point of a application from the point A are (a) (b) (c) (d) 97. Two weights of 10gms and 2 gms hang from the ends of a uniform lever one meter long and weighting 4gms. The point in the lever about which it will balance is from the weight of 10gms at a distance of (a) 5 cm (b) 25 cm (c) 45 cm (d) 65 cm 98. In a right angle and sides a,b,c are respectively 5 cm, 4 cm and 3 cm. If a force has moments 0, 9 and 16 in N-cm. units respectively about vertices A, B and C, then magnitude of is (a) 9 (b) 4 (c) 5 (d) 3 99. If the forces 6W, 5W acting at a point (2, 3) in cartesian rectangular coordinates are parallel to the positive x and y axis respectively, then the moment of the resultant force about the origin is (a) 8W (b) – 3W (c) 3W (d) – 8W 100. A man carries a hammer on his shoulder and holds it at the other end of its light handle in his hand. If he changes the point of support of the handle at the shoulder and if x is the distance between his hand and the point of support, then the pressure on his shoulder is proportional to (a) x (b) (c) (d) 101. If the force represented by is acting through the point , then its moment about the point (1, 3, 1) is (a) (b) – (c) (d) 102. If a couple is acting on 2 particles of mass 1 kg attached with a rigid rod of length 4m, fixed at centre, acting at the end and the angular acceleration of system about centre is 1 rad/s2 , then magnitude of force is (a) 2N (b) 4N (c) 1N (d) None of these 103. Forces P, 3P, 2P and 5P act along the sides AB, BC, CD and DA of the square ABCD. If the resultant meets AD produced at the point E, then AD : DE is (a) 1 : 2 (b) 1 : 3 (c) 1 : 4 (d) 1 : 5 104. If R and are the resultants of two forces and according as they are like or unlike such that then = (a) 2 :1 (b) 3 :4 (c) 4 :3 (d) 1: 2 105. Two like parallel forces P and Q act on a rigid body at A and B respectively. If P and Q be interchanged in positions, show that the point of application of the resultant will be displaced through a distance along AB, where d = (a) (b) (c) (d) 106. A rigid wire, without weight, in the form of the arc of a circle subtending an angle at its centre and having two weights P and Q at its extremities rests with its convexity downwards upon a horizontal plane. If be the inclination to the vertical of the radius to the end at which P is suspended, then = (a) (b) (c) (d) 107. ABCD is a rectangle such that a and . Forces P, P act along AD and CB, and forces Q,Q act along AB and CD. The perpendicular distance between the resultant of forces P, Q at A and the resultant of forces P,Q at C is (a) (b) (c) (d) 108. A horizontal rod AB is suspended at its ends by two vertical strings. The rod is of length 0.6m and weighs 3 Newton. Its centre of gravity G is at a distance 0.4m from A. Then the tension of the string at A is (a) 0.2 N (b) 1.4 N (c) 0.8 N (d) 1 N 109. A horizontal rod of length 5m and weight 4 N is suspended at the ends by two strings. The weights of 8N, 12N, 16N and 20N are placed on the rod at distance 1m, 2m, 3m and 4 m from one end of the rod. The tension in the strings are (a) (b) (c) (d) None of these 110. Two unlike parallel forces P and Q act at points 5m apart. If the resultant force is 9N and acts at a distance of 10m from the greater force P, then (a) (b) (c) (d) 111. A force units act along the line , the moment of the force about the point (4,1) along z-axis is (a) 0 (b) (c) (d) 5 112. The height from the base of a pillar must be end B of a rope AB of given length be fixed so that a man standing on the ground and pulling at its other end with a given force may have the greatest tendency to make the pillar overturn is (a) AB (b) AB/2 (c) (d) None of these 113. In a triangle ABC right angled at C, the lengths of sides AC and BC are 3 cm and 4 cm respectively. Parallel forces each equal to P act at the vertices A,B,C and parallel forces each equal to 2P act at the middle points of all the sides of the triangle. The distance of C.G. from the vertex C is (a) 2/3 cm (b) 4/3 cm (c) 5/3 cm (d) None of these 114. A uniform rod BC of length 6 cm and weight 2 kg can turn freely about the fixed point B. The rod is attached to the point A by a string AC of length 8 cm. The points A and B are in a horizontal line at a distance 10 cm. The tension in the string is (a) 3/5 kg wt (b) 1/5 kg wt (c) 2/5 kg wt (d) None of these 115. If each of the two unlike parallel forces P and Q (P>Q) acting at a distance d apart be increased by S, then the point of application of the resultant is moved through a distance (a) (b) (c) (d) 116. Three forces P, Q and R act along the sides BC, AC and BA of an equilateral triangle ABC. If their resultant is a force parallel to BC through the centroid of the triangle ABC, then (a) (b) (c) (d) 117. Two equal heavy rods, of weight W and length 2a are freely hinged together and placed symmetrically over a smooth fixed sphere of radius r. The inclination of each rod to the horizontal is given by (a) (b) (c) (d) None of these 118. A couple is of moment and the force forming the couple is . If is turned through a right angle, the moment of the couple thus formed is . If instead, the force are turned an angle , then the moment of couple becomes (a) (b) (c) (d) 119. A heavy uniform rod, 15 cm long, is suspended from a fixed point by strings fastened to its ends, their lengths being 9 and 12 cm. If be the angle at which the rod is inclined to the vertical, then (a) (b) (c) (d) 120. A light string of length l is fastened to two points A and B at the same level at a distance ‘a’ apart. A ring of weight W can slide on the string, and a horizontal force P is applied to it such that the ring is in equilibrium vertically below B. The tension in the string is equal to (a) (b) law (c) (d) 121. Two forces P and Q acting parallel to the length and base of an inclined plane respectively would each of them singly support a weight W, on the plane , then = (a) (b) (c) (d) None of these 122. The resultant of the forces 4, 3, 4 and 3 units acting along the lines AB, BC, CD and DA of a square ABCD of side ‘a’ respectively is (a) A force through the centre of the square (b) A couple of moment 7a (c) A null force (d) None of these 123. A body of 6.5 kg is suspended by two strings of lengths 5 and 12 metres attached to two points in the same horizontal line whose distance apart is 13 m. The tension of the strings in kg wt. are (a) 3,5 (b) 2.5, 6 (c) 4, 5 (d) 3, 4 124. A body of mass 10 kg is suspended by two strings 7 cm and 24 cm long, their other ends being fastened to the extremities of a rod of length 25 cm. If the rod be so held that the body hangs immediately below its middle point, then the tension of the strings in kg wt. are (a) 7/5, 24/5 (b) 14/5, 48/5 (c) 3/5, 7/5 (d) None of these 125. A sphere of radius r and weight W rests against a smooth vertical wall, to which is attached a string of length l where one end is fastened to a point on the wall and the other to the surface of the sphere. Then the tension in the string is (a) (b) (c) (d) None of these 126. A system of five forces whose directions and non-zero magnitudes can be chosen arbitrarily, will never be in equilibrium if n of the forces are concurrent, where (a) (b) (c) (d) 127. A string ABC has its extremities tied to two fixed points A and B in the same horizontal line. If a weight W is knotted at a given point C, then the tension in the portion CA is (where a, b, c and the sides and is the area of triangle ABC) (a) (b) (c) (d) 128. A uniform rod of weight W and length 2l is resting in a smooth spherical bowl of radius r. The rod is inclined to the horizontal at an angle of (a) 0o (b) (c) (d) 129. There are three coplanar forces acting on a rigid body. If these are in equilibrium, then they are (a) Parallel (b) Concurrent (c) Concurrent or parallel (d) All of these 130. There is a system of coplaner forces acting on a rigid body represented in magnitude, direction and sense by the sides of a polygon taken in order, then the system is equivalent to (a) A single non-zero force (b) A zero force (c) A couple, where moment is equal to the area of polygen (d) A couple, where moment is twice the area of polygen 131. A weight of 10 N is hanged by two ropes as shown in fig., find tensions and . (a) (b) (c) (d) 132. Three coplanar forces each equal to P, act at a point. The middle one makes an angle of with each one of the remaining two forces. If by applying force Q at that point in a direction opposite to that of the middle force, equilibrium is achieved, then (a) (b) (c) (d) None of these 133. A 2m long uniform rod ABC is resting against a smooth vertical wall at the end A and on a smooth peg at a point B. If distance of B from the wall is 0.3m, then (a) (b) (c) (d) 134. A uniform rod AB movable about a hinge at A rests with one end in contact with a smooth wall. If be the inclination of the rod to the horizontal, then reaction at the hinge is (a) (b) (c) (d) None of these 135. A uniform rod AB, 17m long whose mass in 120kg rests with one end against a smooth vertical wall and the other end on a smooth horizontal floor, this end being tied by a chord 8m long, to a peg at the bottom of the wall, then the tension of the chord is (a) 32 kg wt (b) 16 kg wt (c) 64 kg wt (d) 8 kg wt 136. Forces of magnitudes 3, P, 5, 10 and Q Newton are respectively acting along the sides AB, BC, CD, AD and the diagonal CA of a rectangle ABCD, where AB= 4 m and BC =3m. If the resultant is a single force along the other diogonal BD then P,Q and the resultant are [Roorkee Screening 1991] (a) (b) 5, 6, 7 (c) (d) None of these 137. A uniform rod AB of length a hangs with one end against a smooth vertical wall, being supported by a string of length l, attached to the other end of the rod and to a point of the rod vertically above B. If the rod rests inclined to the wall at an angle , then (a) (b) (c) (d) None of these 138. The resultant of two forces sec B and sec C along sides AB, AC of a triangle ABC is a force acting along AD, where D is (a) Middle point of BC (b) Foot of perpendicular from A on BC (c) D divides BC in the ratio cos B: cos C (d) D divides BC in the ratio cos C: cos B 139. Three coplanar forces each of weight 10 kilogram are acting at a particle. If their line of actions make same angle, then their resultant force will be (a) Zero (b) (c) (d) 20 140. A rough plane is inclined at an angle to the horizon. A body is just to slide due to its own weight. The angle of friction would be (a) (b) (c) (d) 141. A particle is resting on a rough inclined plane with inclination . The angle of friction is , the particle will be at rest if and only if, (a) (b) (c) (d) 142. The relation between the coefficient of friction and the angle of friction is given by (a) (b) (c) (d) 143. A rough inclined plane has its angle of inclination equal to and .The magnitude of the least force in kg wt, parallel to the plane required to move a body of 4kg up the plane is (a) (b) (c) (d) 144. A body of weight W rests on a rough plane, whose coefficient of friction is which is inclined at an angle with the horizon. The least force required to pull the body up the plane is (a) (b) (c) (d) 145. The minimum force required to move a body of weight W placed on a rough horizontal plane surface is (a) (b) (c) (d) 146. A body of weight 4 kg is kept in a plane inclined at an angle of to the horizontal. It is in limiting equilibrium. The coeffiecient of friction is then equal to (a) (b) (c) (d) 147. A cubical block rests on an inclined plane with four edges horizontal. The coefficient of friction is . The block just slides when the angle of inclination of the plane is (a) (b) (c) (d) 148. A weight W can be just supported on a rough inclined plane by a force P either acting along the plane or horizontally. The ratio , for the angle of friction , is (a) (b) (c) (d) None of these 149. A ball AB of weight W rests like a ladder, with upper end A against a smooth vertical wall and the lower end B on a rough horizontal plane. If the bar is just on the point of sliding, then the reaction at A is equal to is the coeffcient of friction) (a) W (b) W (c) Normal reaction at B (d) W/ 150. A body is in equilibrium on a rough inclined plane of which the coeffcient of friction is . The angle of inclination of the plane is gradually increased. The body will be on the point of sliding downwards, when the inclinician of the plane reache (a) (b) (c) (d) 151. A body of weight 40 kg rests on a rough horizontal plane, whose coefficient of friction is 0.25. The least force which acting horizontally would move the body is (a) 10 kg wt (b) 20 kg wt (c) 30 kg wt (d) 40 kg wt 152. The least force required to pull a body of weight W up an inclined rough plane is (a) (b) (c) (d) 153. The foot of a uniform ladder is on a rough horizontal ground and the top rests against a smooth vertical wall. The weight of the ladder is 400 units. A man weighing 800 units stands on the ladder at one quarter of its length from the bottom. If the inclination of the ladder to the horizontal is , the reaction at the wall is (a) 0 (b) (c) (d) 154. A hemi spherical shell rests on a rough inclined plane, whose angle of friction is , the inclination of the plane base of the rim to the horizon cannot be greater than (a) (b) (c) (d) 155. A uniform ladder of length 70m and weight W rests against a vertical wall at an angle of with the wall. The coefficient of friction of the ladder with the ground and the wall are 1/2 and 1/3 respectively. A man of weight W/2 climbs the ladder without slipping. The height in metres to which he can climb is (a) 30 (b) 40 (c) 50 (d) 60 156. A body is on the point of sliding down an inclined plane under its own weight. If the inclination of the plane to the horizon be , the angle of friction will be (a) (b) (c) (d) 157. A ladder 20 ft long is resting against a smooth vertical wall at an angle of with it. Its foot lies on a rough ground with coefficient of friction 0.3. If the weight of the ladder is 30 kg, then a man of 60kg weight can climb on the ladder upto the height of (a) (b) (c) (d) None of these 158. The end of a heavy uniform rod AB can slide along a rough horizontal rod AC to which it is attached by a ring. B and C are joined by a string. If be a right angle, when the rod is on the point of sliding, the coefficient of friction and the angle between AB and the vertical, then (a) (b) (c) (d) 159. A solid cone of semi- vertical angle is placed on a rough inclined plane. If the inclination of the plane is increased slowly and , then (a) Cone will slide down before toppling (b) Cone will topple before sliding down (c) Cone will slide and topple simultaneously (d) Cone will rest in limiting equilibrium 160. A circular cylinder of radius r and height h rests on a rough horizontal plane with one of its flat ends on the plane. A gradually increasing horizontal force is applied through the centre of the upper end. If the coefficient of friction is , the cylinder will topple before sliding, if (a) (b) (c) (d) 161. A uniform beam AB of weight W is standing with the end B on a horizontal floor and end A leaning against a vertical wall. The beam stands in a vertical plane perpendicular to the wall inclined at to the vertical, and is in the position of limiting equilibrium. If the two points of contact are equally rough, then the coefficient of friction at each of them is (a) (b) (c) (d) None of these 162. A ladder, 10 metre long, rests with one end against a smooth vertical wall and the other end on the ground which is rough; the coefficient of friction being . The foot of the ladder being 2 metre from the wall. A man whose weight is 4 times that of the ladder can ascend before it begins to slip a distance (in metre), is (a) (b) (c) (d) None of these 163. A body is pulled up an inclined rough plane. Let be the angle of friction. The required force is least when it makes an angle with the inclined plane, where (a) 1/3 (b) 1/2 (c) 1 (d) 2 164. A body of 6kg rests in limiting equilibrium on an inclined plane whose slope is . If the plane is raised to a slope of , the force in kg along the plane required to support it, is (a) 3 kg (b) (c) (d) 165. The C.G. of three particles placed at the vertices of a triangle is at its (a) Incentre (b) Centroid (c) Circumcentre (d) Orthocentre 166. In a circular disc of uniform metal sheet of radius 10 cm and centre O, two circular holes of radii 5cm and 2.5cm are punched. The centre and of the wholes are on the same diameter of the circular disc. If G is the centre of gravity of the punched disc, then OG= (a) (b) (c) (d) None of these 167. The centre of mass of a rod of length ‘a’ cm whose density varies as the square of the distance from one end, will be at a distance (a) from this end (b) from this end (c) from this end (d) from this end 168. AB is a straight line of length 150cm. Two particles of masses 1kg and 3kg are placed at a distance of 15cm form A and 50 cm from B respectively. The distance of the third particle of mass 2kg from A, so that the C.G. of the system is at the middle point of AB is (a) 40 cm (b) 50 cm (c) 67.5 cm (d) None of these 169. A solid right circular cylinder is attached to a hemisphere of equal base. If the C.G of combined solid is at the centre of the base, then the ratio of the radius and height of cylinder is (a) 1:2 (b) (c) 1: 3 (d) None of these 170. In a right angled triangle one side is thrice the other side in length. The triangle is suspended by a string attached at the right angle. The angle that the hypotenuse of the triangle will make with the vertical is (a) (b) (c) (d) None of these 171. A square hole is punched out of a circular lamina of diameter 4cm, the diagonal of the square being a radius of the circle. Centroid of the remainder from the centre of the circle is at a distance (a) (b) (c) (d) 172. The centre of gravity of the surface of a hollow cone lies on the axis and divides it in the ratio (a) 1 : 2 (b) 1 : 3 (c) 2 : 3 (d) 1 : 1 173. A body consists of a solid cylinder with radius a and height a together with a solid hemisphere of radius a placed on the base of the cylinder. The centre of gravity of the complete body is (a) Inside the cylinder (b) Inside the hemisphere (c) On the interface between the two (d) Outside both 174. The centre of gravity G of three particles of equal mass placed at the three vertices of a right angled isosceles triangle whose hypotenuse is equal to 8 units is on the median through A such that AG is (a) 4/3 (b) 5/3 (c) 8/3 (d) 10/3 175. Weights 2, 3, 4 and 5 lbs are suspended from a uniform lever 6 ft long at distances of 1, 2, 3 and 4 ft from one end. If the weight of the lever is 11 lbs, then the distance of the point at which it will balance from this end is (a) 53/25 (b) 63/25 (c) 73/25 (d) None of these 176. ABC is a uniform triangular lamina with centre of gravity at G. If the portion GBC is removed, the centre of gravity of the remaining portion is at . Then is equal to (a) (b) (c) (d) 177. On the same base AB, and on opposite side of it, isosceles triangles CAB and DAB are described whose altitudes are 12 cm and 6 cm respectively. The distance of the centre of gravity of the quadrilateral CADB from AB, is (a) 0.5 cm (b) 1cm (c) 1.5cm (d) 2cm 178. A straight rod AB of length 1ft balances about a point 5 inches from A when masses of 9 and 6 lbs are suspended from A and B respectively. It balances about a point inches from B when the mass of 6 lbs is replaced by one of 23 lbs. The distance of C.G. of the rod from the end B is (a) inches (b) inches (c) inches (d) None of these 179. A uniform rod of length 2l and weight W is lying across two pegs on the same level ‘a’ ft apart. If neither peg can bear a pressure greater than P, then the greatest length of the rod which may be projected beyond either peg is (a) (b) (c) (d) None of these 180. A rod ft long rests on two pegs 10 inches apart with its centre mid way between them. The greatest masses that can be suspended in succession from the two ends without disturbing equilibrium are 4 and 6 lbs. respectively. The weight of the rod is (a) 2 lbs (b) 4 lbs (c) 3 lbs (d) None of these 181. A heavy rod ACDB, where AC= a and rests horizontally upon two smooth pegs C and D. If a load P were applied at A, it would just disturb the equilibrium. Similar would do the load Q applied to B. If , then the weight of the rod is (a) (b) (c) (d) None of these