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 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 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 relations is true for two unit vector ^𝐴 and ^𝐵 making an angle 𝜃 to each other? (1) ^𝐴+ ^𝐵= ^𝐴- ^𝐵 tan𝜃 (2) ^𝐴- ^𝐵= ^𝐴+ ^𝐵 tan𝜃 2 2 (3) ^𝐴+ ^𝐵= ^𝐴- ^𝐵 cos𝜃 (4) ^𝐴- ^𝐵= ^𝐴+ ^𝐵 cos𝜃 2 2

Q3. A ball is released from a height ℎ. If 𝑡1 and 𝑡2 be the time required to complete first half and second half of the distance respectively. Then, choose the correct relation between 𝑡1 and 𝑡2. (1) 𝑡1 = √2𝑡2 (2) 𝑡1 = √2 - 1𝑡2 (3) 𝑡2 = √2 + 1𝑡1 (4) 𝑡2 = √2 - 1𝑡1

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 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 block of mass 40 kg slides over a surface, when a mass of 4 kg is suspended through an inextensible massless string passing over frictionless pulley as shown below. The coefficient of kinetic friction between the surface and block is 0. 02 . The acceleration of block is: (Given g = 10 m s−2 .) (1) 8 m s−2 (2) 1 m s−2 11 (3) 5 1 m s−2 (4) 54 m s−2

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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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 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. 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. 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