Practice Questions

Q3. A ball of mass 0 . 15 kg hits the wall with its initial speed of 12 m s-1 and bounces back without changing its initial speed. If the force applied by the wall on the ball during the contact is 100 N. calculate the time duration of the contact of ball with the wall. (1) 0 . 018 s (2) 0 . 036 s (3) 0 . 009 s (4) 0 . 072 s

Q3. A block of mass 2 kg moving on a horizontal surface with speed of 4 m s−1 enters a rough surface ranging from x = 0. 5 m to x = 1. 5 m. The retarding force in this range of rough surface is related to distance by F = −kx where k = 12 N m−1 . The speed of the block as it just crosses the rough surface will be (1) 2 m s−1 (2) 2. 5 m s−1 (3) 1. 5 m s−1 (4) zero

Q3. A bag is gently dropped on a conveyor belt moving at a speed of 2 m s−1 . The coefficient of friction between the conveyor belt and bag is 0. 4 Initially, the bag slips on the belt before it stops due to friction. The distance travelled by the bag on the belt during slipping motion is : [Take g = 10 m s−2 ] (1) 2 m (2) 0. 5 m (3) 3. 2 m (4) 0. 8 ms

Q3. A boy ties a stone of mass 100 g to the end of a 2 m long string and whirls it around in a horizontal plane. The string can withstand the maximum tension of 80 N . If the maximum speed with which the stone can revolve is K π rev min−1 . The value of K is : (Assume the string is massless and un-stretchable) (1) 400 (2) 300 (3) 600 (4) 800

Q3. If L, C and R are the self inductance, capacitance and resistance respectively, which of the following does not have the dimension of time? (1) √LC (2) RL (3) CR (4) CL

Q3. Two balls A and B are placed at the top of 180 m tall tower. Ball A is released from the top at t = 0 s. Ball B is thrown vertically down with an initial velocity u at t = 2 s. After a certain time, both balls meet 100 m above the ground. Find the value of u in m s−1 . [use g = 10 m s−2 ] (1) 10 (2) 15 (3) 20 (4) 30

Q3. A balloon has mass of 10 g in air. The air escapes from the balloon at a uniform rate with velocity 4 . 5 cm s-1. If the balloon shrinks in 5 s completely. Then, the average force acting on that balloon will be (in dyne). (1) 3 (2) 9 (3) 12 (4) 18

Q3. Which of the following physical quantities have the same dimensions? (1) Electric displacement →D and surface charge (2) Displacement current and electric field density (3) Current density and surface charge density (4) Electric potential and energy

Q3. A uniform metal chain of mass m and length L passes over a massless and frictionless pulley. It is released from rest with a part of its length l is hanging on one side and rest of its length L −l is hanging on the other side of the pulley. At a certain point of time, when l = Lx , the acceleration of the chain is 2g . The value of x is _____. (1) 6 (2) 2 (3) 1. 5 (4) 4

Q3. A girl standing on road holds her umbrella at 45° with the vertical to keep the rain away. If she starts running without umbrella with a speed of 15√2 km h−1 , the rain drops hit her head vertically. The speed of rain drops with respect to the moving girl is (1) 30 km h−1 (2) 25 km h−1 √2 (3) 30 km h−1 (4) 25 km h−1 √2

Q3. For a free body diagram shown in the figure, the four forces are applied in the ' x' and ' y' directions. What additional force must be applied and at what angle with positive x-axis so that the net acceleration of body is zero? (1) √2 N, 45° (2) √2 N, 135° (3) 2 N, 30° (4) 2 N, 45° √3

Q4. A block of mass M placed inside a box descends vertically with acceleration a. The block exerts a force equal to one-fourth of its weight on the floor of the box. The value of ′a′ will be (1) g (2) 3g 4 (3) g (4) g 2 4

Q4. Potential energy as a function of r is given by U = A −B , where r is the interatomic distance, A and B are r10 r5 positive constants. The equilibrium distance between the two atoms will be : (1) A 15 (2) B 15 ( B ) ( A ) (3) 2A 15 (4) B 15 ( B ) ( 2A )

Q4. For a particle in uniform circular motion, the acceleration →𝑎 at any point 𝑃𝑅, 𝜃 on the circular path of radius 𝑅 is (when 𝜃 is measured from the positive 𝑥-axis and 𝑣 is uniform speed): (1) 𝑣2 𝑣2 (2) 𝑣2 𝑣2 - ^i + ^j - ^i + ^j 𝑅sin𝜃 𝑅cos𝜃 𝑅cos𝜃 𝑅sin𝜃 (3) 𝑣2 𝑣2 (4) 𝑣2 𝑣2 - ^i - ^j - ^i + ^j 𝑅cos𝜃 𝑅sin𝜃 𝑅 𝑅

Q4. A body of mass 0 . 5 kg travels on straight line path with velocity 𝑣= 3𝑥2 + 4 m s-1. The net work done by the force during its displacement from 𝑥= 0 to 𝑥= 2 m is (1) 64 J (2) 60 J (3) 120 J (4) 128 J

Q4. A block of metal weighing 2 kg is resting on a frictionless plane (as shown in figure). It is struck by a jet releasing water at a rate of 1 kg s−1 and at a speed of 10 m s−1 . Then, the initial acceleration of the block, in m s−2 , will be (1) 3 (2) 6 (3) 5 (4) 4

Q4. A ball is released from rest from point P of a smooth semi-spherical vessel as shown in figure. The ratio of the centripetal force and normal reaction on the ball at point Q is A while angular position of point Q is α with respect to point P . Which of the following graphs represent the correct relation between A and α when ball goes from Q to R ? (1) (2) (3) (4)

Q4. Match List-I with List-II List-I List-II Moment of inertia of solid sphere (A) (I) 5 MR2 3 of radius R about any tangent. Moment of inertia of hollow sphere of radius (B) (II) 7 5 MR2 (R) about any tangent. Moment of inertia of circular ring of radius (C) (III) 1 4 MR2 (R) about its diameter. Moment of inertia of circular disc of radius (D) (IV) 1 2 MR2 (R) about any diameter. (1) A −II, B −I, C −IV, D −III (2) A −I, B −II, C −IV, D −III (3) A −II, B −I, C −III, D −IV (4) A −I, B −II, C −III, D −IV

Q4. Sand is being dropped from a stationary dropper at a rate of 0. 5 kg s−1 on a conveyor belt moving with a velocity of 5 m s−1 . The power needed to keep belt moving with the same velocity will be (1) 1. 25 W (2) 2. 5 W (3) 6. 25 W (4) 12. 5 W

Q4. A block of mass M slides down on a rough inclined plane with constant velocity. The angle made by the incline plane with horizontal is θ. The magnitude of the contact force will be : (1) Mg (2) Mg cos θ (3) √Mg sin θ + Mg cos θ (4) Mg sin θ√1 + μ

Q4. A bag of sand of mass 9. 8 kg is suspended by a rope. A bullet of 200 g travelling with speed 10 ms−1 gets embedded in it, then loss of kinetic energy will be (1) 4. 9 J (2) 9. 8 J (3) 14. 7 (4) 19. 6 J

Q4. Two bodies of masses 𝑚1 = 5 kg and 𝑚2 = 3 kg are connected by a light string going over a smooth light pulley on a smooth inclined plane as shown in the figure. The system is at rest. The force exerted by the inclined plane on the body of mass 𝑚1 will be : [Take 𝑔= 10 m s-2] ​ (1) 30 N (2) 40 N (3) 50 N (4) 60 N

Q4. A system of two blocks of masses m = 2 kg and M = 8 kg is placed on a smooth table as shown in figure. The coefficient of static friction between two blocks is 0. 5 . The maximum horizontal force F that can be applied to the block of mass M so that the blocks move together will be (g = 9. 8 m s−2) (1) 9. 8 N (2) 39. 2 N (3) 49 N (4) 78. 4 N

Q4. Water falls from a 40 m high dam at the rate of 9 × 104 kg per hour. Fifty percentage of gravitational potential energy can be converted into electrical energy. Using this hydro electric energy number of 100 W lamps, that can be lit, is (Take g = 10 ms−2 ) (1) 25 (2) 50 (3) 100 (4) 18

Q4. When a ball is dropped into a lake from a height 4. 9 m above the water level, it hits the water with a velocity v and then sinks to the bottom with the constant velocity v . It reaches the bottom of the lake 4. 0 s after it is dropped. The approximate depth of the lake is (1) 39. 2 m (2) 19. 6 m (3) 73. 5 m (4) 29. 4 m