A particle is moving in a circular orbit of radius `r_(1)` with an angular velocity `omega_(1)` It jumps to another circular orbit of radius `r_(2)` and attains an angular velocity `omega_(2)` . If `r_(2)= 0.5 r_(1)` , and if no external torque is applied to the system, then the new angular velocity `omega_(2)` is given by

Options

A. `omega_(2)=omega_(1)`
B. `omega_(2)=2omega_(1)`
C. `omega_(2)=3omega_(1)`
D. `omega_(2)=4omega_(1)`

Answer

D

Explanation

`I_(1)omega_(1)=I_(2)omega_(2)" "mr_(1)^(2)omega_(1)=mr_(2)^(2)omega_(2)`
`therefore r_(1)^(2)omega_(1)=(1)/(4)r_(1)^(2)omega_(2)" "therefore omega_(2)=4omega_(1)`