A particle performing uniform circular motion gas angular momentum `L`. If its angular frequency is double and its kinetic energy halved, then the new angular momentum is :

Options

A. 2 L
B. 4 L
C. L / 2
D. L / 4

Answer

D

Explanation

Rotational kinetic energy, `E=(1)/(2)l omega^(2)=(1)/(2)Lxx 2pin`
`therefore" "E prop L xx n rArr (L_(2))/(L_(1))=(E_(2))/(E_(1))xx(n_(1))/(n_(2))`
`(L_(2))/(L_(1))=[(E_(1)//2)/(E_(1))]xx[(n_(1))/(2n_(1))]`
`l_(2)=(l_(1))/(4)" or "L_(2)=(L)/(4)" "(" as"l_(1)=l)`