Practice Questions

Q2. A person can throw a ball upto a maximum range of 100 m . How high above the ground he can throw the same ball? (1) 25 m (2) 50 m (3) 100 m (4) 200 m

Q2. Two masses 𝑀1 and 𝑀2 are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass 𝑀2 is twice that of 𝑀1. the acceleration of the system is 𝑎1. When the mass 𝑎1 𝑀2 is thrice that of 𝑀1. The acceleration of The system is 𝑎2. The ratio will be 𝑎2 (1) 1 (2) 2 3 3 3 1 (3) (4) 2 2

Q2. A NCC parade is going at a uniform speed of 9 km h-1 under a mango tree on which a monkey is sitting at a height of 19 . 6 m. At any particular instant, the monkey drops a mango. A cadet will receive the mango whose distance from the tree at time of drop is : (Given 𝑔= 9 . 8 m s-2) (1) 5 m (2) 10 m (3) 19 . 8 m (4) 24 . 5 m

Q2. If momentum 𝑃, area 𝐴 and time 𝑇 are taken as fundamental quantities, then the dimensional formula for coefficient of viscosity is (1) PA-1T0 (2) PAT-1 (3) PA-1T (4) PA-1T-1

Q2. Motion of a particle in x −y plane is described by a set of following equations x = 4 sin( π2 −ωt) m and y = 4 sin(ωt) m. The path of the particle will be (1) circular (2) helical (3) parabolic (4) eliptical

Q2. A projectile is projected with velocity of 25 m s−1 at an angle θ with the horizontal. After t seconds its inclination with horizontal becomes zero. If R represents horizontal range of the projectile, the value of θ will be : [use use g = 10 m s−2 ] (1) 1 5t2 (2) 1 4R 2 sin−1( 4R ) 2 sin−1( 5t2 ) (3) tan−1( 4t25R ) (4) cot−1( 20t2R )

Q2. An object of mass 5 kg is thrown vertically upwards from the ground. The air resistance produces a constant retarding force of 10 N throughout the motion. The ratio of time of ascent to the time of descent will be equal to : [Use g = 10 m s−2 ]. (1) 1 : 1 (2) √2 : √3 (3) √3 : √2 (4) 2 : 3

Q2. The SI unit of a physical quantity is Pascal ‐ sec. The dimensional formula of this quantity will be (1) ML2T −1 (2) M −1L3T 0 (3) ML−1T −1 (4) ML−1T −2

Q2. A person is standing in an elevator. In which situation, he experiences weight loss ? (1) When the elevator moves upward with constant (2) When the elevator moves downward with acceleration constant acceleration (3) When the elevator moves upward with uniform (4) When the elevator moves downward with uniform velocity velocity

Q2. Three masses M = 100 kg, m1 = 10 kg and m2 = 20 kg are arranged in a system as shown in figure. All the surfaces are frictionless and strings are inextensible and weightless. The pulleys are also weightless and frictionless. A force F is applied on the system so that the mass m2 moves upward with an acceleration of 2 ms−2 . The value of F is (Take g = 10 ms−2 ) (1) 3360 N (2) 3380 N (3) 3120N (4) 3240N

Q2. Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Two identical balls 𝐴 and 𝐵 thrown with same velocity '𝑢' at two different angles with horizontal attained the same range 𝑅. If A and 𝐵 reached the maximum height ℎ1 and ℎ2 respectively, then 𝑅= 4√ℎ1ℎ2 𝑢2sin2𝜃 𝑢2cos2𝜃 Reason R: Product of said heights. ℎ1ℎ2 = 2𝑔 · 2𝑔 (1) Both A and R are true and R is the correct (2) Both A and R are true but R is NOT the correct explanation of A. explanation of A. (3) A is true but R is false. (4) A is false but R is true.

Q2. A juggler throws balls vertically upwards with same initial velocity in air. When the first ball reaches its highest position, he throws the next ball. Assuming the juggler throws 𝑛 balls per second, the maximum height the balls can reach is 𝑔 𝑔 (1) (2) 2𝑛 𝑛 (3) 2𝑔𝑛 (4) 𝑔 2𝑛2

Q2. At time t = 0 a particle starts travelling from a height 7ˆz cm in a plane keeping z coordinate constant. At any instant of time, it's position along the x and y directions are defined as 3t and 5t3 respectively. At t = 1 s acceleration of the particle will be (1) −30y (2) 30y (3) 3x + 15y (4) 3x + 15y + 7ˆz

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. 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. Arrange the four graphs in descending order of total work done; where W1, W2, W3 and W4 are the work done corresponding to figure a, b, c and d respectively. (1) W3 > W2 > W1 > W4 (2) W3 > W2 > W4 > W1 (3) W2 > W3 > W4 > W1 (4) W2 > W3 > W1 > W4

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. 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. 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 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 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 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. 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