Practice Questions

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

Q3. A disc with a flat small bottom beaker placed on it at a distance 𝑅 from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity 𝜔. The coefficient of static friction between the bottom of the beaker and the surface of the disc is 𝜇. The beaker will revolve with the disc if : (1) 𝑅≤𝜇𝑔 (2) 𝑅≤𝜇𝑔 2𝜔2 𝜔2 𝜇𝑔 𝜇𝑔 (3) 𝑅≥ (4) 𝑅≥ 2𝜔2 𝜔2

Q3. A monkey of mass 50 kg climbs on a rope which can withstand the tension (T) of 350 N . If monkey initially climbs down with an acceleration of 4 m s−2 and then climbs up with an acceleration of 5 m s−2 . Choose the correct option (g = 10 m s−2) (1) T = 700 N while climbing upward (2) T = 350 N while going downward (3) Rope will break while climbing upward (4) Rope will break while going downward

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. 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 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. A body of mass 10 kg is projected at an angle of 45° with the horizontal. The trajectory of the body is observed to pass through a point (20, 10). If T is the time of flight, then its momentum vector, at time t = T , is _____ . √2 [Take g = 10 m s−2 ] N s (1) 100ˆi + (100√2 −200)ˆj N s (2) 100√2ˆi + (100 −200√2)ˆj N s (3) 100ˆi + (100 −200√2)ˆj N s (4) 100√2ˆi + (100√2 −200)ˆj

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

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. 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 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. 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 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. 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. 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 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 ball is projected with kinetic energy E , at an angle of 60° to the horizontal. The kinetic energy of this ball at the highest point of its flight will become : (1) Zero (2) E 2 (3) E (4) E 4