System is shown in the figure. Velocity of sphere A is 9 `(m)/(s)`. Find the speed of sphere B.

Options

A. `2pisqrt((sqrt2l)/(3g))`
B. `2pisqrt((2sqrt2l)/(3g))`
C. `2pisqrt((2l)/(3g))`
D. `3pisqrt((l)/(3g))`

Answer

C

Explanation

`T=2pisqrt((I)/(mgL))`
here `I=(ml^2)/(3)+(ml^2)/(3)=(2mgl^2)/(3)`
From figure, `sin45^@=(L)/((l)/(2))`
`L=(l)/(2sqrt2)` `t=2pisqrt((2ml^2)/(3xx(l)/(2sqrt3)mg))=sqrt((2sqrt2l)/(3g))`