The length of seconds pendulum is 1 m on the earth. If the mass and diameter of the planet is double than that of the earth, then the length of the seconds pendulum on the planet will be

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T p ​ T e ​ ​ = g e ​ ℓ e ​ ​ × ℓ p ​ g p ​ ​ ​ ​ But T e ​ = T p ​ ∴ 1 = g e ​ × ℓ p ​ ℓ e ​ × g p ​ ​ ​ But g p ​ = ( 2 R ) 2 G × 2 M ​ = 4 R 2 GM × 2 ​ = 2 g ​ g e ​ ℓ p ​ = ℓ e ​ g p ​ ℓ p ​ = ℓ e ​ g e ​ g p ​ ​ = 1 × 2 1 ​ = 0.5 m

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