Question

Consider a planet in some system which has a mass double the mass of the earth and density equal to the average density of the earth. If an object weighs W on the earth, then its weight on the planet is:

• A. $W$
• B. $2W$
• C. $\frac{W}{2}$
• D. $2^{1/3}W$

Answer 1

The correct option is D $2^{1/3}W$

Answer is D.

Let m be the mass of the body. Let W be the weight of the body on the earth.
W = mg.
$G=\frac{GM}{R^2}$ (for the earth).
Mass of the planet $=2\times$ (Mass of the earth)
That is, $M^{{}^{\prime }}=2M$.
$\frac{4}{3}\pi {R^{{}^{\prime }}}^3\rho =2\times \frac{4}{3}\pi R^3\rho$.
$R^{{}^{\prime }}={\left(2\right)}^{\frac{1}{3}}\times R$.
So, $W^{{}^{\prime }}={\left(2\right)}^{\frac{1}{3}}\times W$.
Hence, If an object weights $W$ on the earth then its weight on the planet is ${\left(2\right)}^{\frac{1}{3}}\times W$.