PHYSICS-15-10- 11th (PQRS)

XI (PQRS) PHYSICS REVIEW TEST-5 Select the correct alternative. (Only one is correct) [15 × 3 = 45] There is NEGATIVE marking. 1 mark will be deducted for each wrong answer. Q.31 Two trains, which are moving along different tracks in opposite directions towards each other, are put on the same track by mistake. Their drivers, on noticing the mistake, start slowing down the trains when the trains are 300 m apart. Graphs given below show their velocities as function of time as the trains slow down. The separation between the trains after both have stopped, is: (A) 120 m (B) 280 m (C) 60 m (D*) 20 m [Sol. Final separation = Initial separation – |Relative displacement| = 300 – [(1/2) × 40 × 10 + (1/2) × 20 × 8] = 20 m ] Q.32 One end of a thin uniform rod of length L and mass M is riveted to the centre of a uniform circular disc of radius r and mass 2 M so that the rod is normal to the disc. The centre of mass of the combination from the centre of the disc is at distance of L (A) zero (B) 2 M L   2M(0) 2 L (C) 3 L (D*) 6 [Sol. ycm =   M  2M = L/6 ] Q.33 In an electron gun, emission current from the cathode is given by the equation, I  AT 2 eB (KT) [K = Boltzmann constant, A = constant] The dimensional formula for AB2 is same as (A) KT (B) IT2 (C*) IK2 (D) B [Sol. kT is dimensionless  [B] = [kT] Also [I] = [AT2]  [A] = [IT–2]  [AB2] = [IK2] ] IK2 T Q.34 Two long motor boats are moving in the same direction in still water, the boat A with speed of 10km/h and other with a speed of 20km/h. While they are passing each other coal is shoveled from the slower boat to the faster one at a rate 1000kg/min. Assume that the shoveling is always normal relative to the boat A and resistance offered by water is negligible. How much approximate additional force must be provided by driving engine of faster boat (B) if its velocity is to be maintained sconstant (A*) 46N (B) 32N (C) 20N (D) 167 N [Sol. Addition force is required to overcome thrust force dm F = Vrel dt 1000 25 where Vrel = (20 – 10) = 10 km/hr = 10 × 3600 = 9 m/s  F = 25 1000 ×  46 N ] 9 60 Q.35 In a one-dimensional collision, a particle of mass 2m collides with a particle of mass m at rest. If the particles stick together after the collision, what fraction of the initial kinetic energy is lost in the collision? 1 (A) 0 (B*) 3 [Sol. Let initial velocity of 2m is u 1 (C) 2 2 (D) 3  finally, the velocity of the combined mass will be, v = (2m)u 2u 2m  m = 3 1 2 1  2u 2 loss in K.E. (2m)u 2  2 (3m) 3   Initial K.E. =   = 1/3 ] 1 (2m)u2 2 Question No. 36 & 37 (2 questions) A motorcycle moves around a vertical circle with a constant speed under the influence of the force of → gravity W , the force of friction between the wheels and the track f , and the normal force between the → wheels and the track N . Q.36 Which of the following vectors has a constant magnitude? → → → → → (A) N → → → (B) N  f → (C) f  W (D*) N  W  f [Sol. Fnet = → N  W  f → = ma r →  | N  W  f | = m| ar | But centripetal acceleration → has constant magnitude. → →  | N  W  f | = const. ] Q.37 Which of the following vectors, when nonzero, is always directed toward the center of the circle or away from the centre of the circle? → (A) f (B) W → (C*) f  W → (D) N  f → → → [Sol. W  N  f = ma r → W  f → → = ma r – N In the above equation, LHS & RHS are always directed towards or away from the centre. ] Q.38 A ball is released from position A and travels 5m before striking the smooth fixed inclined plane as shown. If the coefficient of restitution in the impact is 1 e = 2 , the time taken by the ball to strike the plane again is (A*) 1s (B) 2 s (C) 2.5 s (D) 3 s [Sol. Just before first collision, speed u = 2g(5) = 10 m/s uy = –10 cos 30° = –53 ux = 10 sin 30° = 5 m/s vx = ux = 5 m/s 5 vy = –euy = 2 3 It strikes the plane again at time, 2vy t = g cos 30 = 1 sec ] Q.39 At t = 0 a particle leaves the origin with a velocity of 6 m/s in the positive y direction. Its acceleration is given by a = 2ˆi  3ˆj m/s2. The x and y coordinates of the particle at the instant the particle reaches maximum y coordinate are (A) 2m, 3m (B*) 4m, 6m (C) 1m, 3m (D) 2m, 6m [Sol. ay = –3 m/s2 & ax = 2 m/s2 It has maximum y-coordinate, when vy = 0 = 6 – 3(t)  t = 2 sec at that instant, y = 1 × 3 × 22 = 6 m 2 & x = 1 × 2 × 22 = 4 m ] 2 Q.40 Figure shows a pendulum of length L suspended form the top of a flat beam of height L/2. The bob is pulled away from the beam so it makes an angle  with the vertical. Now, it is released from rest. If  is the maximum angular deflection to the right, then (A)  =  (B)  <  (C*)  <   2 (D)  > 2 [Sol. Analysing for  < 60° as Lcos > L/2 L In this case Lcos = 2 L + 2 cos  2 cos  = 1 + cos Case I :–  <  cos > cos 1 + cos > 1 + cos 2cos > 1 + cos cos > 1 Not possible Case II :–  >  cos < cos 1 + cos < 1 + cos 2cos < 1 + cos cos < 1 Possible Case III :–  < 2 cos > cos2 1 + cos > 1 + cos2 2cos > 2cos2 1 > cos  Possible Hence,  <  < 2 ] Q.41 In the figure, block 'A' of mass 'm' is attached to one end of a light spring and the other end of the spring is connected to another block 'B' of mass 2m through a light string. 'A' is held and B is at rest in equilibrium. Now A is released. The acceleration of A just after that instant is 'a'. The same thing is repeated for 'B'. In that case the acceleration of 'B' is 'b', then value of a/b is: (A) 0 (B)  (C*) 2 (D) 1/2 [Sol. When Ais held, B will be at rest in equilibrium, if kx = T = 2mg Now, just after A is released When B held and A in equilibrium, T = kx = mg a = 2mg  mg = g m  After B is released,  a/b = 2 ] 2mg  mg b = 2m = g/2 Q.42 In the following figure, what is the minimum coefficient of friction needed between the block & fixed incline so that the system does not move. [Sol. (A) (C) 1 2 T = 10 N (B*) 1 3 (D) Also,  should be atleast such that N + 10 sin 30° = T (10 cos 30°) + 10 sin 30° = 10   = 1/√3 ] Q.43 A square plate has three circular holes of same radius so that centre of each hole is equidistant from the centre of the square plate. A ABC can be formed by joining the centres of the holes as shown in the figure. The plate is placed on a frictionless horizontal surface. If we increase the temperature, then (A*) each side of the triangle will increase and the angle  will remain same (B) each side of the triangle will remain same and the angle  will increase (C) sides of the triangle as well as  will increase (D) sides of the triangle as well as  will remain same [Sol. Distance of centre of each hole from the centre of mass of the plate increase. Also the shown triangle is equilateral and each side increases by same fraction and thus angle  remains constant (= 60°) ] Q.44 10 gm of ice at –20°C is dropped into a calorimeter containing 10 gm of water at 10°C. The specific heat of water is twice that of ice. Neglect heat capacity of the calorimeter. When equilibrium is reached, the calorimeter will contain (A*) 10 gm ice and 10 gm of water (B) 20 gm of water (C) 5 gm ice and 15 gm of water (D) 20 gm ice [Sol. Heat then be given by water, till it reaches 0 °C, Q1 = 10 × S × 10 = 100 S Heat that can be taken by ice to reach 0 °C, Q2 = 10 × (S/2) × 20 = 100 S Q1 = Q2  No ice melts or water freezes ] Q.45 A wire having cross-sectional area S is attached to wall on one side and a block of mass M on the other side which placed on a horizontal surface having coefficient of friction  as shown. Material of wire has coefficient of thermal expansion  and Young's modulus Y. At initial temperature there is no stress in the wire. Now the wire is cooled. At what decrease in temperature the block will begin to move. (A*) Mg YS (B) 2Mg YS (C) Mg 2YS (D) none [Sol. On decreasing, the temperature by () , the tension developed will be T = YS() when about to slip, T = fmax YS() = Mg  = Mg YS ] Select the correct alternative. (One or more than one is/are correct) [3 × 5 = 15] Q.52 When the resultant force on a system of particles is zero, (A) The centre of mass of the system must be at rest (B) Acceleration of each particle may be in the same direction (C*) Velocity of each particle may be in the same direction (D) If onlyone particle has initially non-zero velocity then it is possible that all the particles simultaneously have zero velocity after some time Q.53 Two smooth spheres A and B of equal radii but of masses 1 kg and 2 kg move with speeds 21 m/s and 4 m/s respectively in opposite directions and collide. The velocity of A is reduced to 1 m/s in the same direction. Then, which of the following statements is incorrect? (A) The velocity of B becomes 6 m/s and its direction is reversed (B) The coefficient of restitution is 0.2 (C) The loss of kinetic energy of the system due to the collision is 200 J (D*) The magnitude of impulse applied by the two spheres on each other is 10 Ns [Sol. Before collision After collision By conservation of momentum, 1(21) + 2(–4) = 1(1) + 2(v2) v2 = + 6 m/s  v2 = 6 m/s and its direction is reversed 6 1 e = 21 4 = 0.2 Loss in K.E. =  1 1(21)2  1  2  42  –  1 1 (1)2  1  2  62  = 200 J  2 2   2 2  Impulse on the spheres due to each other = 1 × 21 – 1 × 1 = 20 Ns ] Q.54 A box is accelerating with acceleration = 20 m/s2. A block of mass 10 kg placed inside the box and is in contact with the vertical wall as shown. The friction coefficient between the block and the wall is  = 0.6 and take g = 10 m/s2 (A*) The acceleration of the block will be 20 m/s2 (B*) The friction force acting on the block will be 100 N (C*) The contact force between the vertical wall and the block will be 100 N (D*) The contact force between the vertical wall and the block is only electromagnetic in nature [Sol. N = 10 a = 200 N fmax = 0.6 × 200 = 120 N mg = 100 N < fmax  The friction is static and f = 100 N The contact force = = 100√5 N ] MATCH THE COLUMN [2 × 8 = 16] INSTRUCTIONS: Column-I and column-II contains four entries each. Entries of column-I are to be matched with some entries ofcolumn-II. One or more than one entries of column-I mayhave the matching with the same entries of column-II and one entry ofcolumn-I mayhave one or more than one matching withentries of column-II. Q.5 Quantity Unit (A) Energy density (Energy per unit volume) (P) Dyne/cm2 (B) Force constant of a spring (Q) kg-m/s (C) Pressure (R) Erg/cm2 (D) Area under force-time graph (S) Pascal [Ans. (A) P,S (B) R (C) P, S (D) Q ] Q.6 Ablock is placed on a rough horizontal surface having coefficient of friction . A variable force F = kt,  0  t  mg  acts on it at an angle  to the horizontal.    k sin   Quantities Variation as a function of time (A) Normal reaction (P) (B) Friction (Q) (C) Acceleration (R) (D) Velocity (S) [Sol.(i) N = mg – Fsin = mg – (ksin) t  Graph (Q) for Normal reaction (ii) fmax= N = mg – (k sin) t f = F cos = (k cos) t till F  fmax i.e. for 0  t  mg [Ans. (A) Q (B) S (C) P (D) R] mg k(cos  sin ) for t > k(cos  sin ) f = mg – (ksin) t Hence graph (S) for friction F  f (iii) a = m a = 0 till F  fmax a = k(cos + mg sin) t – g for F  fmax Hence, graph (P) for acceleration (iv) v = 0 till F  fmax v =  a dt t2 = (k cos  + mg sin ) 2 – gt for F  fmax Hence graph (R) for velocity ]