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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 v2. (D) is proportional to v3.
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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