Question

Consider a heavenly body which has a mass twice that of the earth and a radius thrice that of the earth. The weight of a book on this heavenly body, if its weight on the earth is $900\mathrm{N}$ will be :

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

Answer 1

The correct option is D

$200N$

Concept of Acceleration due to gravity:

Acceleration due to gravity of the earth having mass $M$ is given by: $g=\frac{GM}{R^2}$

Here $\mathrm{G}$ is the Universal gravitational constant and $R$ is the radius of the planet.

Weight is given by $\mathrm{W}=\mathrm{mg}$. Here $\mathrm{m}$ is mass and $\mathrm{g}$ is the acceleration due to gravity.

Given data:

Mass of the heavenly body $M\text{'}=2M$ and radius of the heavenly body $R\text{'}=3R$

Acceleration due to gravity on the heavenly body is calculated by

$$\begin{gathered} g\text{'}=\frac{G{M}^{\text{'}}}{R{\text{'}}^2} \\ g\text{'}=\frac{G\times 2M}{(3R{)}^2} \\ g\text{'}=\frac{2GM}{9R^2} \\ g\text{'}=\frac{2g}{9} \end{gathered}$$

Weight on the earth $W=mg=900\mathrm{N}$

Weight on the heavenly body is given by:

$$\begin{gathered} W\text{'}=mg\text{'} \\ W\text{'}=2\mathrm{mg}/9 \\ W\text{'}=(2\times 900)/9 \\ W\text{'}=200\mathrm{N} \end{gathered}$$

Hence, option (D) is correct.