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BITSAT2024PhysicsOscillationsActual

A simple pendulum doing small oscillations at a place R height above earth surface has time period of T₁=4 ~s . T₂ would be it's time period if it is brought to a point which is at a height 2 R from earth surface. Choose the correct relation [ R = radius of Earth ]:

Options

  1. AT₁=T₂
  2. B2 ~T ₁=3 ~T ₂
  3. C3 ~T ₁=2 ~T ₂
  4. D2 ~T ₁= T ₂

Correct answer

C. 3 ~T ₁=2 ~T ₂

Step-by-step solution

Time period of simple pendulum, T =2 l ~g & ~g = GM ( R + h )^2 T ( R + h ) T ₁ ~T ₂ = ( R + h ₁ ) ( R + h ₂ ) = ( R + R ) ( R +2 R ) = 2 3 3 ~T ₁=2 ~T ₂

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