Question

A mass m moves in a circular orbit (centered at the origin) in the field of an attractive central force with potential energy U = krn . Prove that T = nU/2.

Answer 1

Hence the answer T = nU / 2 is proved.

Step-by-step explanation:

U = kr^n

F = -dU / dr

=
`(d)/(dr) kr^(n)`

=
`- knr^(n-1)`

At equation this force is equal to centripetal force.

`- knr^(n-1) = (mv^(2) )/(r)`

`mv^(2) = nkr^(n)`

Total energy = 1/2 mv^2

=
`(1)/(2) nkr^(n)`

=
`n(kr^(n) )/(2)`

`T= (nU)/(2)`