Question

The planet zeta has 2 times the gravitational field strength and sane mass as the earth , how does the radius of zeta compare with the radius of the earth

Answer 1

Gravitational field strength is given by the formula

$g = \frac{GM}{R^2}$

now another planet Zeta is of same mass but double the gravitational strength

$2g = \frac{GM}{r^2}$

now plug in the value of g from above

$2\frac{GM}{R^2} = \frac{GM}{r^2}$

by solving above equation for radius "r"

$r = \frac{R}{\sqrt2}$

so its radius is 0.707R