An object is moving in a circle at constant speed 1'. The magnitude of the rate of change of momentum of the object

(A) is zero. (B) is proportional to v,

(C) is proportional to v². (D) is proportional to v^3.

The correct option is (A) is zero.
Momentum of an object (p) is equal to the mass of the object (m) times velocity of the object (v).
So, p = mv …… (1)

From equation (1) the rate of change of momentum of the object will be,

dp/dt = d/dt (mv)
= m dv/ (2) dt ……


Since the object is moving in a circle at constant speed v (v = constant), therefore the term dv/dt in equation (2) will be equal to zero.

So, dv/dt = 0 …… (3)

Putting the value of equation (3) in equation (2), we get,
dp/dt = m dv/dt
= m×0
= 0 …… (4)
From equation (4) we observed that, the magnitude of the rate of change of momentum of the object is zero. Thus option (a) is correct.