A rod of length `l` forming an angle `theta` with the horizontal strikes a frictionless floor at A with its centre of mass velocity `v_(0)` and no angular velocity. Assuming that the impact at A is perfectly elastic. Find the angular velocity of the rod immediately after the impact.

Options

A. `3/5v_(0)`
B. `4/5v_(0)`
C. `5/3v_(0)`
D. `5/4v_(0)`

Answer

B

Explanation

Let `OA=x, OB=y`
`x^(2)+y^(2)=l^(2)` and `x=lcostheta`
Different `x^(2)+y^(2)=l^(2)` with respect to time.
`2x(dx)/(dt)+2y(dy)/(dt)=0`
`V_(B)=(dy)/(dt)=x/y (dx)/(dt)=-V_(A)cottheta=4/5v_(0)darr`