An astronaut landed on a planet and found that his weight at the pole of the planet was one third of his weight at the pole of the earth. He also found himself to be weightless at the equator of the planet. The planet is a homogeneous sphere of radius half that of the earth. Find the duration of a day on the planet. Given density of the earth `=d_(0).`

Answer

`Tsqrt((9pi)/(2Gd_(0)))`