Question

The kinetic energy of a particle continuously increases with time.

(a) The resultant force on the particle must be parallel to the velocity at all instants.

(b) The resultant force on the particle must be at an angle less than 90° all the time.

(c) Its height above the ground level must continuously decrease.

(d) The magnitude of its linear momentum is increasing continuously.

Answer 1

(b) The resultant force on the particle must be at an angle less than 90° all the time.

(d) The magnitude of its linear momentum is increasing continuously.

Explanation:

Since K.E. of the particle continuously increases, means its velocity continuously increases i.e. it is accelerated. It can only happen if there is a positive component of the resultant force (F.cosθ) along the velocity. For it to happen the resultant force on the particle must be at an angle less than 90° all the time. Hence option (b).

(a) is not true because it is only a special case of the condition in (b) when the angle θ=0° and it need not be a necessary condition.

(c) is not true because the direction of the velocity is not given.

(d) is true because the magnitude of v increases continuously hence the magnitude of linear momentum mv also increases continuously.