Question

A person of mass $M$ IS , sitting on a swing of length $L$ and swinging with an angular amplitude ${\Theta }_0$ . If the person stands up when the swing passes through its lowest point , the work done by him is close to : (assuming that his center of mass moves by a distance $l(l<<L)$) ,

• A. $mgl(1-{\Theta }_0^2)$
• B. $mgl(1+{\Theta }_0^2)$
• C. $mgl$
• D. $Mgl[1+\frac{{\Theta }_0^2}{2}]$

Answer 1

The correct option is B $mgl(1+{\Theta }_0^2)$

Applying law of conservation of angular momentum,

$M{v}^{\prime }(L-l)=mvL\Rightarrow v^{\prime }=\frac{vL}{L-l}$

Using Work-energy theorem,

$W_m=\frac{1}{2}m{v}^{\prime 2}-\frac{1}{2}m{v}^2$

$\Rightarrow W_m=mgl(1+{\Theta }_0^2)$

Hence, option (B) is the correct answer.