1. An athlete in the Olympic game covers a distance of 100m in 10s. His kinetic energy can be estimated in the range?
a) 200J – 500J
b) 2×105J – 3×105J
c) 20000J – 50000J
d) 2000J – 5000J
Explanation: Average speed of the athlete, v = s/t = 10m/s
Assuming the mass of the athlete to 60kg, his average kinetic energy would be
K = 1/2×60×102
K = 3000J.
2. A particle of mass 100g is thrown vertically upwards with a speed of 5m/s. The work done by the force of gravity during the time the particle goes up is ___________
a) 1.25J
b) 0.5J
c) -0.5J
d) -1.25J
Explanation: Work done by the force of gravity = Loss in kinetic energy of the body
Work done by the force of gravity = 1/2 m(v2-u2) = 1/2×100/1000×(02-52)J
Work done by the force of gravity = -1.25J.
3. Statement 1: Linear momentum of a system of particles is zero.
Statement 2: Kinetic energy of a system of particles is zero.
a) 1 does not imply 2 and 2 does not imply 1
b) 1 implies 2 but 2 does not imply 1
c) 1 does not imply 2 but 2 implies 1
d) 1 implies 2 and 2 implies 1
Explanation: When the linear momentum of a system of particles is zero, the velocities of the individual particles may not be zero. The kinetic energy of the system of particles may be non-zero. Thus 1 does not imply 2. When the kinetic energy of the system of particles is zero, then the kinetic energy and hence the velocity of each particle is zero. Therefore the linear momentum of a system of particles is zero. Thus 2 imply 1.
4. A spherical ball of mass 20kg is stationary at the top of a hill of height 100m. It rolls down a smooth surface to the ground, then climbs up another hill of height 30m and finally rolls done to a horizontal base at a height of 20m above the ground. The velocity attained by the ball is ___________
a) 10m/s
b) 10√30m/s
c) 40m/s
d) 20m/s
Explanation: Total energy at 100m height = Total energy at 20m height
mgh1= mgh2 + 1/2 mv2
v = √(2g(h1-h2)) = √(2×10×(100-20)) = 40m/s.
5. If mass-energy equivalence is taken into account when water is cooled to form ice, the mass of water should ___________
a) Increase
b) Remain unchanged
c) Decrease
d) First increase and then decrease
Explanation: The heat energy possessed by water gets converted into mass when ice is formed. This increases the mass. Therefore when water is cooled to form ice, then mass of the water should increase.
6. A body moves a distance of 10m under the action of force F = 10N. If the work done is 25 J, the angle which the force makes with the direction of motion is?
a) 0°
b) 30°
c) 60°
d) None of the mentioned
Explanation: W = Fscosθ
25 = 10×10cosθ
Cosθ = 1/4
θ = cos(-1) 1/4.
7. Two bodies of mass and 4m have equal kinetic energy. What is the ratio of their momentum?
a) 1:4
b) 1:2
c) 1:1
d) 2:1
Explanation: p = √2mK
For same K, p1/p2 = √(m1/m2) = √(m/4m) = 1/2 = 1:2.
8. In stable equilibrium, a body has maximum potential.
a) True
b) False
Explanation: A body is said to be in stable equilibrium if it tends to regain its equilibrium position after being slightly displaced and released. In stable equilibrium, a body has minimum potential energy.
9. On being displaced, the centre of mass of unstable equilibrium goes ___________
a) Higher
b) Neither higher nor lower
c) First higher and then lower
d) Lower
Explanation: A body is said to be in unstable equilibrium if it gets further displaced from its equilibrium position after being slightly displaced and released. In unstable equilibrium, a body possesses maximum potential energy and its centre of mass goes lower on being slightly displaced.
10. Which of the following stays in equilibrium even after being slightly displaced?
a) Stable equilibrium
b) Unstable equilibrium
c) Neutral equilibrium
d) Rigid body
Explanation: If a body stays in equilibrium position even after being slightly displaced and released, it is said to be in neutral equilibrium. When a body is slightly displaced, its centre of mass is neither raised nor lowered and its potential energy remains constant.