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NTA Abhyas JEE Main2020PhysicsCenter of Mass, Momentum and CollisionPractice

A spherical cavity is made in a lead sphere of radius R such that its surface touches the outside surface of lead sphere and passes through the centre. The shift in the centre of mass of the lead sphere as a result of this hollowing, is

Options

  1. AR 7
  2. BR 14
  3. CR 2
  4. DR

Correct answer

B. R 14

Step-by-step solution

Let centre of mass of lead sphere after hollowing be at point O 2 , where OO 2 = x Mass of spherical hollow m = 4 3 π R 2 2 M 4 2 π R 3 = M 8 and x = OO 1 = R 2 ∴ x = M × 0 - M 8 × R 2 M - M 8 = MR 16 7 M 8 = - R 14 ∴ shift = R 1 4

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