question_answer

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, assuming that his centre of mass moves by a distance \[\ell (\ell <<L),\]is close to:                                 [JEE Main Held on 12-4-2019 Morning]

A)  \[Mg\ell \]                     

B)       \[Mg\ell (1+{{\theta }_{0}}^{2})\]

C)  \[Mg\ell (1-{{\theta }_{0}}^{2})\]         

D)       \[Mg\ell \left( 1+\frac{{{\theta }_{0}}^{2}}{2} \right)\]

Correct Answer: B

Solution :

[b] Angular momentum conservation.

Now,

By, Binomial approximation

here, maximum velocity

So,