Question

The mass of Mars is $1/9$ times that of the Earth & radius is $1/2$ times that of the Earth. What is the weight of a body on Mars, having a mass of $1000\text{kg}$ ?

• A. $4356\text{N}$
• B. $6653\text{N}$
• C. $4500\text{N}$
• D. $5200\text{N}$

Answer 1

The correct option is A $4356\text{N}$


As per the information

Mass of earth, $M_e=M$;

Mass of Mars, $M_m=\frac{M}{9}$

Radius of Earth, $R_e=R$

Radius of Mars, $R_m=\frac{R}{2}$

Acceleration due to gravity on Earth is given by

$g_e=\frac{G{M}_e}{R_e^2}=\frac{GM}{R^2}=g$

Similarly, acceleration due to gravity on Mars is

$g_m=\frac{G{M}_m}{R_m^2}=\frac{4}{9}\frac{GM}{R^2}=\frac{4}{9}g$

$\therefore$ weight of the body on Mars will be

$W_m=m{g}_m=1000\times \frac{4}{9}\times 9.8$

$\therefore W_m=4356\text{N}$

Hence, option $\left(a\right)$ is correct.