Question

The mass and diameter of a planet are twice those of earth. What will be the time period of that pendulum on this planet,wwhich is second's on the earth?

Answer 1

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.

Note: All the parameters with subscript ‘2’ are for Earth and those with subscript ‘3’ are for the new planet.

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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