A particle of mass m has position vector r = a(cosωt, sinωt). The direction of the net force on the particle is:
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Question

A particle of mass m has position vector r = a(cosωt, sinωt). The direction of the net force on the particle is:

G1 Physics · Accepted Answer

The position vector is r = a(cosωt, sinωt), so the particle moves on a circle of radius a with constant angular speed ω. Differentiate twice: a v e c a_vec a v ​ ec = d²r/dt² = -ω²r. Therefore, F = m a v e c a_vec a v ​ ec = -mω²r. Hence the force is always directed toward the centre, i.e. opposite to the position vector r. Correct option: A.