Practice Questions

Q2. Train A is moving along two parallel rail tracks towards north with 72 km h-1 and train 𝐵 is moving towards south with speed 108 km h-1. Velocity of train 𝐵 with respect to 𝐴 and velocity of ground with respect to 𝐵 are (in m s-1): (1) -30 and 50 (2) -50 and -30 (3) -50 and 30 (4) 50 and -30

Q2. Time periods of oscillation of the same simple pendulum measured using four different measuring clocks were recorded as 4.62 s, 4.632 s, 4.6 s and 4.64 s. The arithmetic mean of these readings in correct significant figure is : (1) 5 s (2) 4.623 s (3) 4.6 s (4) 4.62 s

Q2. Projectiles 𝐴 and 𝐵 are thrown at angles of 45° and 60° with vertical respectively from top of a 400 m high tower. If their times of flight are same, the ratio of their speeds of projection 𝑣𝐴: 𝑣𝐵 is: (1) 1: √3 (2) √2: 1 (3) 1: 2 (4) 1: √2

Q2. A particle moving in a straight line covers half the distance with speed 6 m/s. The other half is covered in two equal time intervals with speeds 9 m/s and 15 m/s respectively. The average speed of the particle during the motion is : (1) 10 m/s (2) 8 m/s (3) 9.2 m/s (4) 8.8 m/s

Q2. A body starts moving from rest with constant acceleration covers displacement S1 in first (p −1) seconds and S2 in first p seconds. The displacement S1 + S2 will be made in time : (1) (2p + 1) s (2) √(2p2 −2p + 1) s (3) (2p −1) s (4) (2p2 −2p + 1) s

Q3. A 2 kg brick begins to slide over a surface which is inclined at an angle of 45∘ with respect to horizontal axis. The co-efficient of static friction between their surfaces is: (1) 1.7 (2) 1 √3 (3) 0.5 (4) 1

Q3. A body travels 102.5 m in nth second and 115.0 m in (n + 2)th second. The acceleration is : (1) 6.25 m/s2 (2) 12.5 m/s2 (3) 9 m/s2 (4) 5 m/s2

Q3. A stone of mass 900 g is tied to a string and moved in a vertical circle of radius 1 m making 10 rpm. The tension in the string, when the stone is at the lowest point is (if π2 = 9. 8 and g = 9. 8 m s−2 ) (1) 97 N (2) 9. 8 N (3) 8. 82 N (4) 17. 8 N

Q3. A given object takes n times the time to slide down 45∘ rough inclined plane as it takes the time to slide down an identical perfectly smooth 45∘ inclined plane. The coefficient of kinetic friction between the object and the surface of inclined plane is : (1) √1 − n21 (2) 1 −n2 (3) 1 − 1 (4) √1 −n2 n2

Q3. A body of weight 200 N is suspended from a tree branch through a chain of mass 10 kg. The branch pulls the chain by a force equal to (if g = 10 m/s2 ) : (1) 100 N (2) 200 N (3) 300 N (4) 150 N

Q3. The relation between time ‘𝑡’ and distance ‘𝑥’ is 𝑡= 𝛼𝑥2 + 𝛽𝑥, where 𝛼 and 𝛽 are constants. The relation between acceleration 𝑎 and velocity 𝑣 is: (1) 𝑎= - 2𝛼𝑣3 (2) 𝑎= - 5𝛼𝑣5 (3) 𝑎= - 3𝛼𝑣2 (4) 𝑎= - 4𝛼𝑣4

Q3. A cricket player catches a ball of mass 120 g moving with 25 m s-1 speed. If the catching process is completed in 0 . 1 s then the magnitude of force exerted by the ball on the hand of player will be(in SI unit): (1) 24 (2) 12 (3) 25 (4) 30

Q3. A train is moving with a speed of 12 m s−1 on rails which are 1. 5 m apart. To negotiate a curve radius 400 m, the height by which the outer rail should be raised with respect to the inner rail is (Given, g = 10 m s−2 ): (1) 6. 0 cm (2) 5. 4 cm (3) 4. 8 cm (4) 4. 2 cm

Q3. If the radius of curvature of the path of two particles of same mass are in the ratio 3 : 4, then in order to have constant centripetal force, their velocities will be in the ratio of: (1) √3 : 2 (2) 1 : √3 (3) √3 : 1 (4) 2 : √3

Q3. A train starting from rest first accelerates uniformly up to a speed of 80 km/h for time t , then it moves with a constant speed for time 3t. The average speed of the train for this duration of journey will be (in km/h ) : (1) 40 (2) 80 (3) 30 (4) 70

Q3. A light string passing over a smooth light fixed pulley connects two blocks of masses 𝑚1 and 𝑚2. If the 𝑔 acceleration of the system is 8, then the ratio of masses is (1) 9 (2) 8 7 1 4 5 (3) (4) 3 3

Q3. A 1 kg mass is suspended from the ceiling by a rope of length 4 m . A horizontal force ' F ' is applied at the mid point of the rope so that the rope makes an angle of 45∘ with respect to the vertical axis as shown in figure. The magnitude of F is : (Assume that the system is in equilibrium and g = 10 m/s2 ) (1) 10 N (2) 10 N √2 (3) 1 N (4) 1 N 10×√2 J energy is supplied to the satellite,

Q3. A particle moving in a circle of radius 𝑅 with uniform speed takes time 𝑇 to complete one revolution. If this particle is projected with the same speed at an angle 𝜃 to the horizontal, the maximum height attained by it is equal to 4𝑅. The angle of projection 𝜃 is then given by : (1) 12 (2) 𝜋2𝑅 12 sin−12𝑔𝑇2 sin−1 𝜋2𝑅 2𝑔𝑇2 (3) 12 (4) 𝜋𝑅 12 cos−12𝑔𝑇2 cos−1 𝜋2𝑅 2𝑔𝑇2

Q3. All surfaces shown in figure are assumed to be frictionless and the pulleys and the string are light. The acceleration of the block of mass 2 kg is: (1) g (2) g 3 (3) g (4) g 2 4

Q3. Three blocks 𝐴, 𝐵 and 𝐶 are pulled on a horizontal smooth surface by a force of 80 N as shown in figure. The tensions 𝑇1 and 𝑇2 in the string are respectively: (1) 40N, 64N (2) 60N, 80N (3) 88N, 96N (4) 80N, 100N

Q3. If G be the gravitational constant and u be the energy density then which of the following quantity have the dimensions as that of the √uG : (1) pressure gradient per unit mass (2) Gravitational potential (3) Energy per unit mass (4) Force per unit mass

Q3. A light unstretchable string passing over a smooth light pulley connects two blocks of masses m1 and m2 . If the acceleration of the system is g , then the ratio of the masses m2 is : 8 m1 (1) 8 : 1 (2) 5 : 3 (3) 4 : 3 (4) 9 : 7

Q3. A man carrying a monkey on his shoulder does cycling smoothly on a circular track of radius 9 m and completes 120 resolutions in 3 minutes. The magnitude of centripetal acceleration of monkey is ( in m/s2 ) : (1) 57600π2 ms−2 (2) Zero (3) 4π2 ms−2 (4) 16π2 ms−2

Q4. The bob of a pendulum was released from a horizontal position. The length of the pendulum is 10 m . If it dissipates 10% of its initial energy against air resistance, the speed with which the bob arrives at the lowest point is: [Use, g = 10 m s−2 ] (1) 6√5 m s−1 (2) 5√6 m s−1 (3) 5√5 m s−1 (4) 2√5 m s−1

Q4. A block of mass 𝑚 is placed on a surface having vertical cross section given by 𝑦= 𝑥2 . If coefficient of friction 4 is 0 . 5, the maximum height above the ground at which block can be placed without slipping is: 1 1 (1) m (2) m 4 2 (3) 1 m (4) 1 m 6 3