The mass and radius of a planet are double that of the earth. If time period of a simple pendulum on the earth is T, find the time period on the planet.

Explanation

Mass of the planet, `M_(P)=2M_(e):`
Radius of planet, `R_(P)=2R_(e)`
Time period of pendulum on earth`=T,`
`g_(e)=(GM)/(R^(2)),g_(p)=(G.2M)/((2R)^(2))=(GM)/(2R^(2))=(g_(e))/(2)`
`T=2pisqrt(l/g),` on the earth, `T'=2pisqrt((l)/(g_(p))`, on the planet
`therefore T'/T=sqrt((g_(e))/(g_(p))=sqrt2 or T'=sqrt2T`