A particle of mass is under the influence of the gravitational field of a body of mass ( )

PHYSICS · Single correct · CBSE · Physics · Laws of Motion · Laws of Motion

Problem

A particle of mass

m

is under the influence of the gravitational field of a body of mass

M

(

\gg m

). The particle is moving in a circular orbit of radius

r_0

with time period

T_0

around the mass

M

. Then, the particle is subjected to an additional central force, corresponding to the potential energy

V_c(r) = m\alpha/r^3

, where

\alpha

is a positive constant of suitable dimensions and

r

is the distance from the center of the orbit. If the particle moves in the same circular orbit of radius

r_0

in the combined gravitational potential due to

M

and

V_c(r)

, but with a new time period

T_1

, then

(T_1^2 - T_0^2)/T_1^2

is given by.

G

is the gravitational constant. (A)

\frac{3\alpha}{GMr_0^2}

(B)

\frac{\alpha}{2GMr_0^2}

(C)

\frac{\alpha}{GMr_0^2}

(D)

\frac{2\alpha}{GMr_0^2}