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

Options

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

Answer

B

Explanation

Here `E=(1)/(2)Iomega^(2)=(1)/(2)Iomega.omega`
`E=(1)/(2)xxL.omega`
or `L=(2E)/(omega)orLprop(E)/(omega)`
Similarly `L.=(2E.)/(omega.)=(2xx(E)/(2))/(2omega)=(2E.)/(4omega.)=(E)/(2omega)`
`therefore (L.)/(L)=((E)/(2omega))/((2E)/(omega))=(1)/(4)`
or `L.=(L)/(4)`