The mass and diameter of a planet are twice those of earth wt is gravity
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Let the mass be M, acceleration due to gravity g, length of pendulum string l, time period be T and universal gravitational constant be G
g=GM/r²
g₂=GM₂/r₂²
g₃=GM₃/r₃²
Since M₃=2M₂andr₃=2r₂
g₃=2GM₂/4r₂²
g₃=GM₂/2r₂²
g₃=g₂/2
NowT=2π√(l/g)
T₂=2π√(l/g₂)
T₃=2π√(l/g₃)
T₃=2π√(2l/g₂²)
T₃=√2.T₂
Hence, the time period of a pendulum will become √2 times its original value on the new planet.
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