A particle of mass m is moving in a circular orbit of radius r in a force field given by `vec(F)=-(K)/(r^(2))hat(r)` . The angular momentum L of the particle about the centre varies as

Options

A. `L prop sqrtr`
B. `L prop r^(3//2)`
C. `L prop (1)/(sqrtr)`
D. `L prop r^(1//3)`

Answer

A

Explanation

`(mv^(2))/(r)= (K)/(r^(2)) rArr v= sqrt((K)/(mr))`
`L= mvr = sqrt(mrK)` Thus we get `L prop sqrtr`