In the shown diagram two point masses m are joined by a massless rod of length 5.5m. The lower end of the mass sytem is dragged with constant velocity `V_(0)` rightwards the magnitude of velocity of centre of mass when `theta=37^(0)`, will be

Options

A. `(5v_(0))/(6)`
B. `2v_(0)`
C. `v_(0)sqrt(2)`
D. `(6v_(0))/(5)`

Answer

A

Explanation

`x^(2)+y^(2)=l^(2)`
`(dy)/(dt)=-(x)/(y)((dx)/(dt))`
if `theta=37^(@)`
`(dy)/(dt)=-(x)/(y)(dx)/(dt)=-(4)/(3)v_(@)`
`vecv_(cm)=(mv_(@)hati-m(4v_(@))/(3)haty)/(2m)`
`|vecV_(cm)|=(5v_(@))/(6)`