Practice Questions

Q3. A stone of mass m, tied to a string is being whirled in a vertical circle with a uniform speed. The tension in the string is (1) the same throughout the motion. (2) minimum when the rope is in the horizontal position. (3) minimum at the highest position of the circular path. (4) minimum at the lowest position of the circular path.

Q3. A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration ac is varying with time t as ac = k2rt2 , where k is a constant. The power delivered to the particle by the force acting on it is - (1) Zero (2) 2mk2r2t (3) mk2r2t (4) 2mk2rt

Q3. If t = √x + 4, then ( dxdt )t=4 is: (1) 4 (2) Zero (3) 8 (4) 16

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 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. 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. 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. An object is thrown vertically upwards. At its maximum height, which of the following quantity becomes zero ? (1) Momentum (2) Potential energy (3) Acceleration (4) Force

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

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

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. 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. As per the given figure, two blocks each of mass 250 g are connected to a spring of spring constant 2 N m−1 . If both are given velocity v in opposite directions, then maximum elongation of the spring is (1) v (2) v 2√2 2 (3) v (4) v 4 √2

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. 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 body of mass 8 kg and another of mass 2 kg are moving with equal kinetic energy. The ratio of their respective momenta will be (1) 1: 1 (2) 2: 1 (3) 1: 4 (4) 4: 1

Q4. A block of mass 10 kg starts sliding on a surface with an initial velocity of 9. 8 ms−1 . The coefficient of friction between the surface and block is 0. 5 . The distance covered by the block before coming to rest is :[use g = 9. 8 ms−2 ] (1) 9. 8 m (2) 4. 9 m (3) 12. 5 m (4) 19. 6 m →Q5. + x −y plane. Assume distance in A particle experiences a variable force F = (4xˆi 3y2ˆj) in a horizontal meters and force is newton. If the particle moves from point (1, 2) to point (2, 3) in the x −y plane, then Kinetic Energy changes by : (1) 25 J (2) 50 J (3) 12. 5 J (4) 0 J

Q4. A bullet of mass 200 g having initial kinetic energy 90 J is shot inside a long swimming pool as shown in the figure. If it's kinetic energy reduces to 40 J within 1 s, the minimum length of the pool, the bullet has to travel so that it completely comes to rest is (1) 45m (2) 90m (3) 125m (4) 25m

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 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. 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

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. If force →F = 3 ^𝑖+ 4 ^𝑗- 2 ^𝑘 acts on a particle having position vector 2 ^𝑖+ ^𝑗+ 2 ^𝑘 then, the torque about the origin will be: (1) -10 ^i + 10 ^j + 5 ^k (2) 3 ^i + 4 ^j - 2 ^k (3) 10 ^i + 5 ^j - 10 ^k (4) 10 ^i + ^j - 5 ^k

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. 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