A uniform chain AB of mass m and length l is placed with one end A at the highest point…

Physics · JEE Advanced · NTA Exams — Work, Energy and Power

A uniform chain AB of mass m and length l is placed with one end A at the highest point of a hemisphere of radius R. Referring to the top of the hemisphere as the datum level, the potential energy of the chain is (given that \(\ell<\frac{\pi R}{2}\))
   
  1. \(\frac{m R^{2} g}{\ell}\left(\frac{\ell}{R}-\sin \frac{\ell}{R}\right)\)
  2. \(\frac{m R^{2} g}{2 \ell}\left(\frac{\ell}{R}-\sin \frac{\ell}{R}\right)\)
  3. \(\frac{m R^{2} g}{2 \ell}\left(\sin \frac{\ell}{R}-\frac{\ell}{R}\right)\)
  4. \(-\frac{m R^{2} g}{\ell}\left(\frac{\ell}{R}-\sin \frac{\ell}{R}\right)\)

Answer

(D) - m R^ 2 g ( R - R )

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