A particle is acted upon by a force of a constant magnitude which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane. It follows that ?

A.

Its velocity is constant and kinetic energy is constant

B.

Its acceleration and velocity is constant

C.

Its kinetic energy is constant and it moves in a circular path

D.

Its acceleration is constant and it moves in a circular path

Answer: Option C

Explanation:

For a particle in uniform circular motion, the direction of both velocity and acceleration vectors change continuously but their magnitudes remain unchanged. The kinetic energy is not affected. Hence its kinetic energy is constant and it moves in a circular path.

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

Answer: Option D

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 = 1/2×60×10^{2} K = 3000J.

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

Answer: Option D

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(v^{2}-u^{2}) = 1/2×100/1000×(0^{2}-5^{2})J Work done by the force of gravity = -1.25J.

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

Answer: Option C

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.

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

Answer: Option A

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.