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Classical Mechanics Level 3

Two spherical objects each of radii R R and masses m m and M M are suspended using two strings of equal length ℓ \ell as shown below (assume ℓ > > R \ell >> R ). What is the angle φ \varphi which the mass M M makes with the vertical approximately equal to?

Original problem: KVPY 2015 SB/SX

2 m R ( m + M ) ℓ \dfrac{2mR}{(m+M)\ell} m R ( m + M ) ℓ \dfrac{mR}{(m+M)\ell} M R ( m + M ) ℓ \dfrac{MR}{(m+M)\ell} 2 M R ( m + M ) ℓ \dfrac{2MR}{(m+M)\ell}

Tapas Mazumdar by Tapas Mazumdar , 20, India

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