1. The decrease in potential energy of a ball of mass 20kg, which falls from a height of 50cm, is?
a) 968J
b) 98J
c) 1980J
d) 450J
Explanation: U = mgh
U = 20×9.8×0.50 = 98J.
2. If the water falls from a dam into a turbine wheel 19.6m below, then the velocity of water at the turbine is? (g=9.8m/s)
a) 9.8m/s
b) 19.6m/s
c) 39.2m/s
d) 98m/s
Explanation: Loss in potential energy = Gain in kinetic energy
mgh = 1/2mv2
v = √2gh = √(2×9.8×19.6)=19.6m/s.
3. Two particles are seen to collide and move jointly together after the collision. During such a collision, for the total system ___________
a) Neither the mechanical energy nor the linear momentum is conserved
b) Mechanical energy is conserved, but not the linear momentum
c) Both the mechanical energy and the linear momentum are conserved
d) Linear momentum is conserved, but not the mechanical energy
Explanation: The collision is inelastic. Only momentum is conserved and not mechanical energy. There is a loss of kinetic energy in such a collision.
4. When a body moves with a constant speed along a circle ___________
a) No work is done on it
b) No acceleration is produced in it
c) Its velocity remains constant
d) No force acts on it
Explanation: For a body in uniform circular motion, the centripetal force acts perpendicular to the circular path.
5. A gun fires a bullet of mass 50g with a velocity of 30m/s. Because of this, the gun is pushed back with a velocity of 1m/s. The mass of the gun is?
a) 5.5kg
b) 3.5kg
c) 1.5kg
d) 0.5kg
Explanation: By conservation of momentum, MV = mv
M = mv/V = 1.5kg.
6. A body of mass 5kg is raised vertically to a eight of 10m by a force of 170N. The velocity of the body at this height will be ___________
a) 37m/s
b) 22m/s
c) 15m/s
d) 9.8m/s
Explanation: W = Gain in potential energy+Gain in kinetic energy
Fh = mgh + 1/2 mv2
170×10=5×10×10+1/2×5×v2
v = √480 = 22m/s.
7. A position dependent force, F = 7-2x+3x2-N acts on a small body of mass 2kg and displaces it from x = 0 to x = 5m. The work done in joules is ___________
a) 135
b) 270
c) 35
d) 70
Explanation: W = ∫Fdx = \(\int_0^5 (7-2x+3x^2)dx = [7x-x^2+x^3]_0^5\)
W = 35-25+125=135J.
8. A particle of mass M is moving in a horizontal circle of radius R with uniform speed v. When it moves from one point to a diametrically opposite point, its ___________
a) Kinetic energy changes by (Mv)2/4
b) Momentum does not change
c) Momentum changes by 2Mv
d) Kinetic energy changes by (Mv)2
Explanation: At any two diametrically opposite points, velocities of the particle have the same magnitude but opposite directions. Therefore change in momentum = Mv-(-MV)=2Mv.
9. Two identical balls A and B collide head on elastically. If velocities of A and B, before the collision are +0.5m/s and -0.3m/s respectively, then the velocities after the collision, are ___________
a) -0.5m/s and +0.3m/s
b) +0.5m/s and +0.3m/s
c) +0.3m/s and -0.5m/s
d) -0.3m/s and +0.5m/s
Explanation: In an elastic collision between two bodies of equal masses, velocities get exchanges after collision. vA=-0.3m/s and vB=+0.5m/s.
10. The kinetic energy acquires by a mass m in travelling distance d, starting from rest, under the action of a constant force is directly proportional to ___________
a) m
b) m0
c) √m
d) 1/√m
Explanation: v2-u2=2as
v2-0=2×F/m×d = 2Fd/m
Kinetic energy = 1/2 mv2=1/2 m×2Fd/m = Fd
Hence, kinetic energy does not depend on m or it is directly proportional to m0.