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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 v 2 . (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.
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