Question

A planet has density same as that of Earth and mass is twice that of Earth. If the weight of an object on Earth is "W" then the weight on the planet is:

• A. $2^{\frac{2}{3}}W$
• B. $2^{\frac{1}{3}}W$
• C. $2^{\frac{4}{3}}W$
• D. $W$

Answer 1

Answer: (B)

$2^{\frac{1}{3}}W$

Answer 2

The correct option is(B): $2^{\frac{1}{3}}W$

Planet with the mass M has radius as R and Planet with mass 2M has radius as R'
$\rho \frac{4}{3}\pi R^{3}=M$
$\rho \frac{4}{3}\pi R'^{3}=2M$
$\Rightarrow R'=2^{\frac{1}{3}}R$
$=2\frac{GM}{2^{\frac{2}{3}}R^{2}}=2^{\frac{1}{3}}\frac{Gm}{R^{2}}=2^{\frac{1}{2}}W$
$W'=2^{\frac{1}{3}}W$