Physics - Gravitation Question with Solution | TestHub

The formula for acceleration due to gravity is 

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

Let the density of earth and planet be $\rho$, and the radius of the planet be $R\text{'}$. Let $R$ be the radius of the earth and $g$ be the acceleration due to gravity of earth and $g\text{'}$ be the acceleration due to gravity of planet.

So, the masses are

$M=\frac{4}{3}\pi R^3\rho ...\left(i\right)$

$M\text{'}=\frac{4}{3}\pi {\left(R\text{'}\right)}^3\rho ...\left(ii\right)$

So, $\frac{g\text{'}}{g^{}}=\frac{{\displaystyle \frac{GM\text{'}}{R{\text{'}}^2}}}{{\displaystyle \frac{GM}{{\displaystyle R^2}}}}=\frac{M\text{'}}{M}{\left(\frac{R}{R\text{'}}\right)}^2 ...\left(iii\right)$

From equation (i) and (ii) we get $R\text{'}=2^{\frac{1}{3}}R$

Substituting the value in equation (iii),

$\frac{g\text{'}}{g}=\left(2^1\right)2^{\frac{-2}{3}}=2^{\frac{1}{3}}g$

Weight is given by $W\text{'}=mg\text{'}=2^{\frac{1}{3}}W$