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 M omega^2 L^2 = Mgl(1 - cos theta_0)`
`omega^2L = 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 - 2 cos theta_0]l`
`W = mg [3 - 2(1 -(theta_0^2))/(2)]l , " "W = Mg [3 - 2 + 2 xx(theta_0^2)/2] l , W = Mg [1 + theta_0^2]l , " "W = Mgl[1 + theta_0^2]`.