JEE Main | 2018Work, Power and EnergyHard

Question

A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the nth power of R. If the period of rotation of the particle is T, then,

Options

A.

T∝Rn2+1

B.

T∝R(n+1)/2​​​​​​​

C.

T∝Rn/2

D.

T∝R3/2 for any n

Solution

mω2R = Force∝1Rn
⇒ ω2∝1Rn+1
⇒ ω∝1Rn+12
time period T = 2πω∝ Rn+12

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