A particle is moving with a uniform speed in a circular orbit of radius in a central…

PHYSICS · Single correct · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics

Problem

A particle is moving with a uniform speed in a circular orbit of radius

R

in a central force inversely proportional to the

n^{\text{th}}

power of

R

. If the period of rotation of the particle is

T

, then: (1)

T \propto R^{3/2}

for any

n

. (2)

T \propto R^{n/2+1}

(3)

T \propto R^{(n+1)/2}

(4)

T \propto R^{n/2}