Question

A planet in solar system has a mass double that of earth and density equal to that of earth. An object weigh W on the earth, will weigh on the other planet as $W^1$. Then:

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

Answer 1

The correct option is D $W^1=2^{\frac{1}{3}}W$

$M_p=2M_E$

$\Rightarrow \frac{4}{3}\pi R_p^3\delta =2\times \frac{4}{3}\pi R_p^3\delta \Rightarrow R_p=2^{1/3}\left(R\right)$

Weight , W$=$mg $\Rightarrow W\propto g$

But g$=\left(\frac{4}{3}\pi \delta GR\right)\Rightarrow g\propto R$

$\Rightarrow W\propto g\Rightarrow \frac{W_1}{W_2}=\frac{R_1}{R_2}$

$\Rightarrow \frac{W}{W^1}=\frac{R}{2^{1/3}R}=\frac{1}{2^{1/3}}\Rightarrow W^1=2^{1/3}\left(W\right)$