Correct Answer - A::D
Consider the bug at point `P` at any time `t`, moving with speed `v` along the stick, so `L=mvhmvlsintheta costhetaimplies ` Angular momentum of bug
about pooint `O`
`impliestau=(dL)/(dt)=(mlsintheta cos theta)(dv)/(dt)`
`impliesmg(l-x)costheta=(mlsintheta costheta)(dv)/(dt)`
`implies(dv)/(dt)=g/(sintheta)(1-x/l)`
`implies(dv)/(dt)+g/(lsintheta)x =g/(sintheta)implies` Equation of SHM with mean position at point `A`
`impliesT=2pisqrt((lsintheta)/g)`
Time required `=T/4=(pi)/2 sqrt((lsintheta)/2)`