A ring of mass m and radius R is rolling on a horizontal plane. If the ring suddenly starts rotating about its diameter, then its angular velocity in this will be

Options

A. `(V)/( R)`
B. `(2V)/( R)`
C. `(V)/(2R)`
D. `sqrt2(V)/( R)`

Answer

B

Explanation

`KE_("roll")=KE_("rot")`
`(1)/(2)mv^(2)(1+(k^(2))/(R^(2)))=(1)/(2)m omega^(2)`
`mv^(2)(1+(k^(2))/(R_(2)))=(mR^(2))/(4)omega^(2)`
`omega =(2v)/(R )`