Question

Imagine a new planet having the same density as that of the earth but it is 3 times bigger than the earth in size . If the acceleration due to gravity on the surface of the earth is $g$ and that on the new planet is $g^{\prime }$, then what is the value of $\frac{g^{\prime }}{g}$

Answer 1

$g^{\prime }=\frac{GM}{R^{\prime 2}}=\frac{G\frac{4}{3}\pi R^{\prime 3}\rho }{R^{\prime 2}}=\frac{4G\pi R^{\prime }\rho }{3}$
$g^{\prime }=\frac{4G\pi \left(3R\right)\rho }{3}=3g($ Since$,g=\frac{4G\pi R\rho }{3})$