Editable Study Material for JEE, NEET, CBSE and Foundation by STUDYINNOVATIONS.COM

1. (c) 2. (b) 3. (c) 4. (d) 5. (b) 6. (b) 7. (a) 8. (d) 9. (c) 10. (b) 11. (c) 12. (d) 13. (a) 14. (a) 15. (d) 1. (a) 2. (b) 3. (d) 4. (b) 5. (c) 6. (b) 7. (b) 8. (a) 9. (a) 10. (a) 11. (c) 12. (c) 13. (b) 14. (c) 15. (c) 1. 6 cm. along O O from the sphere of smaller radius. (1 e)u2 sin 2 2. g 4. 5 m/sec. 5. 10 2 m / sec. at 45º with x-axis. 9 1 6. 2 100 7. 3 metre 8. t = 155 second v = 2681 m/s. 9. mg 11. 18.29 m/sec2. 13. momentum is conserved. 14. bob will not rise because whole momentum is transferred to the body at rest. 15. speed will remain constant. SUBJECTIVE LEVEL - II 2. (i) murel m  M (ii) ML m  M 2u sin   1  u2 sin 2 3. (i) g  1 e  (ii) g(1 e) (iii)   tan1(en tan ) 4. m2   M 2 5.  M  m  l 6. 3mv2 7. 0.167 N-s 1 M2 mV2 8. 2 (m  2M)2 d 9. 1  e2 10. Vsphere= V(eM  msin2 ) (M  msin2 ) mvsin (1  e) Vwedge= (M  msin2 ) . SUBJECTIVE LEVEL - III Mv2...

PROBLEMS 1.. A car P is moving with a uniform speed of 5 (3½) m/s to- C wards a carriage of mass 9 kg at rest kept on the rails at a point B as shown in fig. The height AC is 120 m. Cannon P balls of kg are fired from the car with an initial velocity 100 A m/s at an angle 300 with the horizontal. The first cannon B ball hits the stationary carriage after a time t0 and sticks to it. Determine t0. AT t0 , the second connon ball is fired. Assume that the resistive force between the rails and the carriage is constant and ignore the vertical motion of the carriage throughout. If the second ball also hits and sticks to the carriage, what will be the horizontal velocity of the carriage just after the second impact? 2. One a frictionless horizontal surface, assumed to be the x-y plane, y as small trolley A is moving along a straight lien parallel to the y- A axis (see figure) with a constant velocity of  1 m/s. At a particular instant, when the line OA makes an angle of 45º wi...

(BRUSH UP YOUR CONCEPTS) 1. Two smooth spheres A and B, of equal radius but mass m and M, are free to move on a horizontal table. A is projected with speed u towards B which is at rest. On impact, the line joining their centres is inclined at an angle  to the velocity of A before impact. If e is the coefficient of restitution between the spheres, find the speed with which B begins to move. If A’s path after impact is perpen- dicular to its path before impact, show that tan 2   eM  m . M  m 2. A man of mass m moves on a plank of mass M with a constant velocity urel . with respect to the plank, as shown in figure. (i) If the plank rests on a smooth horizontal surface, then deter- mine its velocity with respect to ground. (ii) If the man travels a distance L with respect to the plank, then L find the distance traveled by the plank with respect to ground. 3. An imperfectly elastic particle is projected from a point in a horizontal place with velocity u at an angle  to the horizon....

C.B.S.E. SUBJECTIVE LEVEL - I (REVIEW YOUR CONCEPTS) 1. Two solid spheres of radii 6 cm and 12 cm and masses 36 g & 18 g respectively touch each other. What is the position of centre of mass of the combination? 2. A projectile is fired with a speed u at an angle  above a horizontal field. The coefficient of restitu- tion of collision between the projectile and the field is e. How far from the starting point, does the projectile makes its second collision with the field? 3. Prove that the CM of two particles lies between the particles on a line that connects the two par- ticles. 4. A 3 kg mass moving at a speed of 15 ms-1 collides with a 6 kg object initially at rest. They stick together. Find the velocity of the combination after the collision. 5. Two ice skaters, A and B, approach each other at right angles. Skater A has a mass of 50 kg and she is traveling in the + x direction at 2 ms-1. Skater B has a mass of 40 kg and he is moving in the + y direction at 2.5 ms-1. Th...

OBJECTIVE LEVEL - I 1. If the KE of a body becomes four times of its initial value, then the new momentum will be : (a) three times its initial value (b) four times its initial value (c) twice its initial value (d) unchanged. 2. A shell explodes and many pieces fly off in different directions. The following is conserved : (a) Kinetic energy (b) Momentum (c) Neither momentum nor KE (d) Momentum and KE. 3. Which one of the following statement is true : (a) Momentum is conserved in elastic collisions but not in inelastic collision (b) Total KE is conserved in elastic collisions but momentum is not (c) Total KE is not conserved but momentum is conserved in inelastic collision (d) KE and momentum both are conserve in all types of collisions. 4. A bag of mass M hangs by a long thread and a bullet (mass m) comes horizontally with velocity v and gets caught in the bag. Then for the combined system (bag + bullet) : (a) Momentum is mMv/(M+m) (b) KE is (1/2)Mu2 (c) Momentum is mv(M+m) /M (...

SUBJECTIVE SOLVED PROBLEMS 1. Locate the centre of mass of a uniform semicircular rod of radius R and linear density λ kg/m. Solution: From the symmetry of the body we see that the CM must lie along the y axis, so xCM = 0. In this case it is convenient to express the mass element in terms of the angle θ , measured in radians. The element, which subtends an angle dθ at the origin, has a length R dθ and a mass dm = λ R dθ . Its y coordinate is y = R sin θ . ydm Therefore, yCM = M yCM = 1 λR 2 sin θdθ  M 0 λR 2 M [cosθ ]π  2λR 2 M 2R x The total mass of the ring is M = π R λ ; Therefore, yCM = π . 2. Find the centre of mass of a uniform solid hemisphere of radius R and mass M with centre of sphere at origin and the flat of the hemisphere in the x, y plane. Solution: Let the center of the sphere be the origin and let the flat of the hemisphere lie in the x, y plane as shown. By symmetry x  y  0. Consider the hemisphere divided into a series of slices parallel to x, ...

OBJECTIVE SOLVED 1. Hail storms are observed to strike the surface of the frozen lake at 300 with the vertical and rebound at 600 with the vertical. Assume contact to be smooth, the coefficient of restitution is : (a) e  1 (b) e  1 3 (c) Ans. (b) e  (d) e = 3. Solution: Components of velocity before and after collision parallel to the plane are equal, So v sin 60 = u sin 30 ...(1) Components of velocity normal to the plane are related to each other v cos 60 =e u (cos 30) ...(2)  cot 60 = e cot 30  e  cot 60 cot 30 1  e  3  e  1 . 3 2. Two particles of masses m1 and m2 in projectile motion have velocities → and → respectively at time t = 0, They collide at time t . Their velocities become → and → at time 2t while still moving 0 v1 v2 0 in air. The value of  →  →    →  →  is : (a) 0 (c) 2 m1  m 2 gt 0 Ans. (c) m1v'1 m 2 v'2 m1v1 m 2 v 2 (b) (b) (d) m1  m 2 gt 0 2 m1  m 2 gt 0 . ...