A simple pendulum, made of a string of length \( \ell \) and a bob of mass \( \mathrm{m} \), is ...

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A simple pendulum, made of a string of length \( \ell \) and a bob of mass \( \mathrm{m} \), is released from a small angle \( \theta_{0} \). It strikes a block of mass M, kept on a horizontal surface at its lowest point of oscillations, elastically. It bounces back and goes up to an angle \( \theta_{1} \). Then \( M \) is given by :
(1) \( \frac{\mathrm{m}}{2}\left(\frac{\theta_{0}+\theta_{1}}{\theta_{0}-\theta_{1}}\right) \)
(2) \( \mathrm{m}\left(\frac{\theta_{0}-\theta_{1}}{\theta_{0}+\theta_{1}}\right) \)
(3) \( \mathrm{m}\left(\frac{\theta_{0}+\theta_{1}}{\theta_{0}-\theta_{1}}\right) \)
(4) \( \frac{m}{2}\left(\frac{\theta_{0}-\theta_{1}}{\theta_{0}+\theta_{1}}\right) \)
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