Practice Questions

Q2. Two cars are travelling towards each other at speed of 20 m s−1 each. When the cars are 300 m apart, both the drivers apply brakes and the cars retard at the rate of 2 m s−2 . The distance between them when they come to rest is : (1) 200 m (2) 100 m (3) 50 m (4) 25 m

Q2. A particle is moving in a straight line. The variation of position x as a function of time t is given as x = (t3 −6t2 + 20t + 15) m. The velocity of the body when its acceleration becomes zero is: (1) 4 m s−1 (2) 8 m s−1 (3) 10 m s−1 (4) 6 m s−1

Q2. The equation of stationary wave is : y = 2a sin ( 2πntλ ) cos ( 2πxλ ). Which of the following is NOT correct : (1) The dimensions of n/λ is [T] (2) The dimensions of n is [LT−1] (3) The dimensions of x is [L] (4) The dimensions of nt is [L]

Q2. A bullet is fired into a fixed target looses one third of its velocity after travelling 4 cm. It penetrates further 𝐷× 10-3 m before coming to rest. The value of 𝐷 is : (1) 32 (2) 5 (3) 3 (4) 4

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 projected vertically upwards with a certain speed from the top of a tower reaches the ground in t1 . If it is projected vertically downwards from the same point with the same speed, it reaches the ground in t2 . Time required to reach the ground, if it is dropped from the top of the tower, is : (1) √t1t2 (2) √t1 + t2 (3) √t1 −t2 (4) √t1t2

Q2. The angle of projection for a projectile to have same horizontal range and maximum height is : (1) tan−1(4) (2) tan−1 ( 14 ) (3) tan−1 ( 21 ) (4) tan−1(2)

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. 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. Given below are two statements : Statement (I) : The limiting force of static friction depends on the area of contact and independent of materials. Statement (II) : The limiting force of kinetic friction is independent of the area of contact and depends on materials. In the light of the above statements, choose the most appropriate answer from the options given below : (1) Statement I is correct but Statement II is incorrect (2) Statement I is incorrect but Statement II is correct (3) Both Statement I and Statement II are incorrect (4) Both Statement I and Statement II are correct

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. 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. 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

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 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 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 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. 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 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. A clock has 75 cm, 60 cm long second hand and minute hand respectively. In 30 minutes duration the tip of second hand will travel x distance more than the tip of minute hand. The value of x in meter is nearly (Take π = 3.14 ) : (1) 140.5 (2) 118.9 (3) 139.4 (4) 220.0

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. 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 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