A person of mass M is setting 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, assuming that his centre of mass moves by a distance `l(lt lt L)`

Options

A. `Mgl`
B. `Mgl(1-theta_(0)^(2))`
C. `Mgl(1+(theta_(0)^(2))/(2))`
D. `Mgl(1+theta_(0)^(2))`

Answer

D

Explanation

`W=M(g+a)l," "a=omega^(2)L`
`(1)/(2)Momega^(2)L^(2)=Mg(1-cos theta_(0))," "omega^(2)L=2g(1-cos theta_(0))`
`W=M[g+2g(1-cos theta_(0))]l, " "w=M[g+2g-2g cos theta_(0)]l`
`W=mg[3-2costheta_(0)]l," "W=mg[3-2(1-(theta_(0)^(2))/(2))]l`
`W=Mg[3-2+2xx(theta_(0)^(2))/(2)]l`
`Wg[1+theta_(0)^(2)]l," "W=Mgl[1 +theta_(0)^(2)]`