PHYSICS-15-10- 11th (PQRS) SOLUTION

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 due to a 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 when both have stopped, is: (A) 120 m (B) 280 m (C) 60 m (D*) 20 m 1 [Sol: x1 = 2 1 × 10 × 40 = 200 m; x2 = – 2 × 8 × 20 = –80 m  xreletive = x1 + x2 = 280  separation = 300 – 280 = 20 m (D) ] 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 L (C) 3 L (D*) 6 [Sol: xcm = 2M (0) + M  L  L   = ] 2M + M 6 Q.33 In an electron gun, emission current from the cathode is given by the equation, I = AT2 e(B (KT)) [K = Boltzmann constant, A = constant] The dimensional formula for AB2 is same as (A) KT (B) IT2 (C*) IK2 (D) [Sol: [A] = IT–2; (B) = KT  [AB2] = IK2 (C) ] 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 perfectly side ways and resistance offered by water is negligible. How much approximate additional force must be provided by driving engine of faster boat (B) if speed of boat remains constant (A*) 46N (B) 32N (C) 20N (D) 167 N [Sol: extra momentum needed per second is the force applied 1000 50 In 1 sec. M = 60 = 3 kg 10 1000 25 v = 60  60 = 9 m/s  F = Mv = 50  25  46 N ] 3 9 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 1 (C) 2 2 (D) 3 [Sol: 2mu + 0 = 3mV  V = 2 u 3 (Momentum conservation) 1 1  2 2 2 Ki = 2 (2m)u2 + mu2, Kf = 2 (3m)  3 u   Kf = 3 mu2   K Ki  K f 1  Ki = Ki = mu2 = 3 ] 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 quantities has a constant magnitude? (A) N (B) N + f (C) f + W (D*) N + W + f [Sol: N + W + f is the centripetal force here mV 2 | N + W + f | = r = const. (D) ] Q.37 Which of the following quantities, 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: So, f + W (C) ] Q.38 The ball is released from position Aand 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: v = 2· = 10m/s 2 Tf =   5 = 1s 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: ux = 0, uy = 6 & ax = 2, ay = –3 At ymax = Vy = 0  0 = 6 – 3t  t = 2S  x = u t + 1 a t2 = 4m x 2 x 1 y = u t + a t2 = 6m y 2 y (B) ] Q.40 A simple pendulum has a string of length l and bob of mass m. When the bob is at its lowest position, it is given the minimum horizontal speed necessary for it to move in a circular path about the point of suspension. When the string is horizontal the net force on the bob is (A) mg (B) 3mg (C*) 10mg (D) 4mg [Sol: Minimum speed at lowest point  V = = 3mg speed at horizontal position = = = mg ] Q.41 In the figure a block 'A' of mass 'm' is attached at 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 has obtained equilibrium. Now Ais 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: In Ist case In 2nd Case 2mg  mg T = 2mg a = m kx = mg b = 2mg  mg 2m  a = g   b = g/2   a = 2 b (C) ] 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. (A) (C) 1 2 (B*) 1 3 (D) 2 [Sol: T = g For block A  T < g sin300 + N (for block B) N = gcos300  g < g 3 2 + g 2  N = g 3 2   < 1  min = 3 (B) ] Q.43 An aluminium rod of Young’s modulus 7 × 109Nm–2 has a breaking strain of 0.2%. The minimum cross- sectional area of the rod in m2 in orde to support a load of 7 ×103 N is (A) 5 ×10–5 m2 (B*) 5 ×10–4 m2 (C) 5 ×10–3 m2 (D) 5 ×10–2 m2 [Sol: B = YB = 7 × 109 × 0.2 100 = 14 × 106 N/m2 W 7 103 W = BA  A =  = 6 = 5 × 10–4 m2 ] B 1410 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: Assume Tf = 00C & M gm ice melts (0 < M < 10) Qice = 10 × 0.5 × 20 + M· 80 = 100 + 10 M Qwater = 10 × 1 × 10 = 100 Qice = Qwater  M = 0  Tf = 00C with 10 gm ice & 10 gm water ] Q.45 The co-efficient of thermal expansion of a rod is temperature dependent and is given by the formula  = aT, where a is a constant and T in °C. If the length of the rod l at temperature 0°C, then the temperature at which the length will be 2l is: (A) 1 dl dl (B*) 2l dl T 1 (C) a 2 (D) a [Sol: a =  l dT l = dT   l =  aTdT 0  ln2 = aT 2  = 2 Select the correct alternative. (One or more than one is/are correct) [3 × 5 = 15] Q.52 An object follows a curved path. The following quantities may remain constant during the motion. (A*) speed (B) velocity (C*) acceleration (D*) magnitudeofacceleration 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 speed of A is reduced to 1 m/s in the same direction as that of its initial 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: Pi = Pf  1·(21) + 2·(–4) = 1 ·(1) + 2 ·(V)  V = 12 = 6m / s 2  Velocity of B becomes 6m/s & direction reversed velocity of e = velocity of separation approach = 6 1 21+ 4 = 0.2 K = 1 × 1 × (21)2 + i 2 1 × 2 × 42 = 236.5 J 2 Kf = 1 × 1 × 12 + 2 1 × 2 × 62 = 36.5 J 2  K = Ki – Kf = 200 J change in momentum of A = 1.21 – 1.1 = 20 N  Impulse applied by two spheres on each other = 20 N ] Q.54 A car is accelerating with acceleration = 20 m/s2. A box of mass 10 kg is placed inside the car is in contact with the vertical wall as shown. The friction coefficient between the box and the wall is  = 0.6 and take g = 10 m/s2 (A*) The acceleration of the box will be 20 m/s2 (B*) The friction force acting on the box will be 100 N (C*) The contact force between the vertical wall and the box will be 100 5 N (D*) The net contact force between the vertical wall and the box is only of electromagnetic in nature [Sol: fmax = N = 0.6 × 200 = 120 N applied force 100 N < fmax  The block is stationary w.r.t. car so, in ground frame ablock = 20m/s2 (same as car) frictional force = applied force = 100N contact force CF = contact force is electromagnetic in nature  (A), (B), (C), (D) ]  CF = 100 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 of column-II. One or more than one entries of column-I mayhave the matching with the same entries of column-II and one entryof column-I mayhave one or more than one matching with entries 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) [Ans. (A) Q (B) S (C) P (D) R] [Sol: N = mg – kt sin mg at t = k sin   N = 0 & at t = 0  N = mg N – t graph (A  Q) at VOS kt cos = N  t1 = kt cos – N = ma mg K (cos +  sin )  kt cos – (mg – ktsin) = ma K (cos +  sin )  a = m t – g (1) upto, t = t1, friction will increase linearly with applied force t > t1  f = N (B  S) (C) upto t = t1 , a = 0 for t > t1 a varies as equation (1) C  P (D) upto t = t1, V = 0 t > t1  a = Mt + C dV  dt = Mt + C M k (cos +  sin ) 2  V = 2 t2 + Ct = (D)  R t  gt 2m