Question

A rod of length $L$ is held vertically on a smooth horizontal surface. The top end of the rod is given a gentle push and it starts slipping down. At a certain instant of time, when the rod makes an angle of ${37}^o$ with horizontal, the velocity of COM of the rod is $2m{s}^{-1}$. Find the velocity of the end of the rod in contact with the horizontal surface at that instant?

• A. $2m{s}^{-1}$
• B. $1m{s}^{-1}$
• C. $4m{s}^{-1}$
• D. $1.5m{s}^{-1}$

Answer 1

The correct option is D $1.5m{s}^{-1}$

initial L about A=$0$

Final about A=$0$

$2\times \frac{l}{2}=x\times lx=1v.cos53=xv\frac{3}{5}=1v=\frac{5}{3}\simeq 1.5m/s$