Question

Consider a heavenly body which has a mass twice that of the Earth and radius thrice that of the Earth. What will be the weight of the book on this heavenly body, if its weight on the Earth is $900N$?

• A. $400N$
• B. $600N$
• C. $500N$
• D. $200N$

Answer 1

The correct option is D $200N$

Let the mass of book be $m$ & its weight on the heavenly body be $W_h$.
Given, mass of heavenly body = $2M_e$
Radius of heavenly body = $3R_e$
Thus, $W_h=\frac{G\left(2M_e\right)m}{(3R_e{)}^2}$
$W_h=\frac{G\left(2M_e\right)m}{9R_e^2}$ $\cdots \left(1\right)$
$W_e=G\frac{M_{e}m}{R_e^2}$ $\cdots \left(2\right)$
Dividing equation (1) by equation (2) we get
$\frac{W_h}{W_e}=\frac{2}{9}\Rightarrow \frac{W_h}{900}=\frac{2}{9}$
$W_h=200N$