Practice Questions and Solutions
Q1. Two balls of same size, mass 2 Kg and another of mass 4 Kg are dropped simultaneously from a building of height 70m. When they are 1m above the ground, the two balls have the same A). acceleration B). momentum C). kinetic energy D). potential energy E). velocity Ans. (A) is the correct choice. Since both the balls have different masses and the velocity of a falling body goes on increasing, so momentum, K.E., and P.E. of both the balls can not be same. So, all other options are incorrect. Both the spheres fall with the same acceleration equal to acceleration due to gravity. Q2.A man caught a tennis ball of mass150g moving at the speed of 20 ms1 . If the catching process is completed in 0.1s, the force of blow exerted by the ball on the hand of the player is equal to A).3N B).30N
C).150N D).300N E).250N Ans. (B) is the correct choice. Impulse (Ft) =change in momentum=mu- mv Therefore, F= (mu-mv)/t = (0.150 x 20 – 0)/0.1=30N Q3. The potential energy of a long spring when stretched by 2 cm is P. If the spring is stretched by 8 cm, the potential energy in it is A) 16P B) 8P C) 4P D) P/4 E) P/8 Ans. (A) is the correct choice. P=1/2Kx2=1/2K x 4=2K Therefore, K=P/2. When x=8cm P’=1/2Kx2=1/2 x (p/2) x 64=16P Q4. In a uniform circular motion, the work done by the centripetal force is A).Greater than zero B). infinite C). zero D).less than zero
E).varies at different points of circular motion. Ans. (C) is the correct choice.
W=FMcos θ, θ=900 Therefore FMcos 900=0 Q5. Which of the following graphs shows variation of P.E (P) with position x. (A)
(B)
(C)
(D)
(E)
Ans. (C) is the correct choice. Potential energy P=1/2 Kx2. Q6. In a head on elastic collision of a very heavy body moving at v with a light body at rest, velocity of heavy body after collision is A). v/2 B) v C). 2v D). v2 E). 0 Ans. (B) is the correct choice. V 1 = (2 m 2 u 2 + u 1[m 1-m 2])/ (m 1 +m 2) V 2 =2 m 1 u 1 +u 2(m 2-m 1)/ (m 1+m 2) U 1 = 0 and u 2 =v, m2>m 1, Therefore, v 1 =2m 2 v/m 2=2v and v 2 =v m 2 /m 2=v
Q7.Two bodies of mass m and 2m have equal kinetic energies. The ratio of their linear momentum is A).1/2 B).1 C).0 D).√2 E). 1/√2 Ans. (E) is the correct choice. E 1=p 1 2/2 m 1=p 1 2/2m E 2 = p 2 2/2m 2=p 2 2/4m since, E 1=E 2 Therefore (p 1/p 2 ) 2=1/2 Or p 1 / p2 =1/√2. Q8. A sphere of mass 2 Kg and another sphere of mass 4Kg are dropped together from a 60m tall building. After fall of 30m each towards the earth, their respective kinetic energies will be in the ratio of A).1:1 B).2:1 C).1:2 D).1:3 E).3:1 Ans. (C) is the correct choice. The speed of both the spheres after falling through 30m will be same i.e. v 1= v 2 (v=√2gh) Therefore (K.E) 1/ (K.E) 2=1/2(m 1v 1 2)/1/2 (m 2 v 2 2 )=m 1/ m 2 =1/2
Q9. A sphere of mass 500g moving on a horizontal smooth surface, collides with a weightless spring of force constant K= 50Nm -1. The maximum compression of the spring would be
A).15m B).0.5m C).0.15m D).1.05m E).1.5m Ans. (E) is the correct choice. K.E of sphere=elastic potential energy of compressed spring i.e.1/2mv 2=1/2Kx 2, where x = compression of the spring Therefore, x = √9m/K)v 2 =√(0.5/50)x 225=1.5m Q10. If K is the kinetic energy of a projectile fired at an angle 45 0, then its kinetic energy at highest position is A).K/2 B).K/4
C).K D).2K E).4K Ans. (A) is the correct choice. Velocity of ball at the highest point, v = u cos 450=u/√2 Therefore, K.E at the highest point=1/2m v2 =1/2m x (u/2) 2 =1/2(m u 2 /4) =1/4(1/2mu2 ), since ½ m u 2 = K Therefore K.E at the highest point is k/2. Q11. Two blocks of mass 8kg and 4kg are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of 12 ms-1 to the heavier block in the direction of the lighter block. The velocity of the centre of mass is A). 4ms-1 B). 6ms-1 C). 12ms-1 D).10ms-1 E). 8ms-1 Ans. (E) is the correct choice. Vcm= (m1v1 +m2v2)/m1+m2=8 x 12 +4 x0/8 +4=8ms-1 Q12.A 20Kg sphere moving with a velocity 6 ms-1 collides with a 30Kg sphere initially at rest. If both of them coalesce, then the final velocity of the combined mass will be A).1.2 ms -1 B).2.4 ms -1
C).3.6 ms -1 D).5 ms -1 E). 6 ms -1 Ans. (B) is the correct choice. According to law of conservation of linear momentum m 1 u 1 +m 2 u 2 = (m 1 +m 2 )V Therefore, V= (m1u1+m2u2)/m1+m2= (20x6+0)/50=120/50=2.4 ms-1 Q13. A particle of mass m moving with a velocity v makes an elastic collision with another particle of the same mass which is initially at rest. The velocity of the first particle after collision is A). V B).-V C).-2V D).0 E).V/2 Ans. (D) is the correct choice. Two bodies of same mass interchange their velocities after elastic collision. Q14. n small balls, each of mass m make elastic collision with a surface, are with a velocity u. The force experienced by the surface will be A).mnu B).2mnu C).4mnu
D).mnu/2 E).mnu/4 Ans. (A) is the correct choice. Force=rate of change of momentum= (mu)/(1/n)=mnu. Q15. If W 1, W 2, W 3 represent the work done in moving a particle from X position to Y position along three different paths 1,2,3 respectively as shown in the figure in the gravitational field of a point mass m .The correct relation between W 1,W2,W3 will be
A). W1>W2>W3 B). W1W1>W3 D).W1=W2=W3 E).W2