A particle performing uniform circular motion has angular momentum L. If its angular frequency is halved and its kinetic energy is doubled, then the new angular momentum is

Options

A. `(L)/(4)`
B. `2L`
C. `4L`
D. `(L)/(2)`

Answer

C

Explanation

Angular momentum , `L = I omega " " …. (i)`
Kinetic energy , ` K = (1)/(2) I omega^(2) = (1)/(2) L omega " "` (Using (i))
`therefore L = (2K)/(omega)`
When `omega` is halved and K is doubled , the new angular momentum becomes
`L. = (2(2K))/((omega//2)) = (4 (2K))/(omega) = 4L " "` (Using (ii))