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

Options

A. `T prop R^((n + 1))""^(/2)`
B. `T prop R^(n//2)`
C. `T prop R^(3//2)` for any n
D. `T prop R^((n)/(2)+1)`

Explanation

According to the given condition, `F prop = (1)/(R^(n))`
or, `F= (k)/(R^(n)) " " or, m omega^(2) R = (k)/(R^(n))`
or, `" "m((2pi)/(T))^(2) = (k)/(R^(n+1)) " " or, (4pi^(2)m)/(T^(2)) = (k)/(R^(n + 1))`
So, `(1)/(T^(2)) prop (1)/(R^(n + 1)) " "or, T prop R^((n+1)/(2))`
The option A is correct.