Statement I: A pendulum is taken from Earth to a planet having four times Earth's mass and twice Earth's radius; its time period remains the same. Statement II: The time period of a simple pendulum depends only on the gravity of the planet.
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Question

Statement I: A pendulum is taken from Earth to a planet having four times Earth's mass and twice Earth's radius; its time period remains the same. Statement II: The time period of a simple pendulum depends only on the gravity of the planet.

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G1 Physics · Accepted Answer

g′=G(4M)/(2R)²=g, so for the same length the period is unchanged. But T=2π√(l/g), so T depends on both l and g. Thus I is true and II is false.