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 2R from earth surface. Choose the correct relation [R = radius of Earth]:
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Question

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 2R from earth surface. Choose the correct relation [R = radius of Earth]:

Options

G1 Physics · Accepted Answer

At height R above Earth's surface, distance from Earth's centre is 2R. At height 2R, distance is 3R. Acceleration due to gravity varies as: g' ∝ 1/r² For a simple pendulum: T ∝ 1/√g' Therefore: T ∝ r So: T₁/T₂ = 2R/3R = 2/3 Hence: 3T₁ = 2T₂