Question

The radius of earth is about 6400 km and that of mars is 3200 km. The mass of the earth is 10 times the mass of mars. An object weight 200 N on the surface of earth. Its weight on the surface of mars will be.
(A) 80 N
(B) 40 N
(C) 20 N
(D) 8N

Answer 1

Hint
Weight is nothing but the force exerted by an object on the earth due to its gravitational pull. The acceleration due to gravity is different for different planets. It is given by, $g = \dfrac{{G{m_e}}}{{{r_e}^2}}$. Take the ratio of the acceleration due to gravity of earth with respect to mars to find g on mars. Now multiply this value with the mass to calculate the mass of the object on mars.

Complete step by step answer
The value of acceleration due to gravity in terms of gravitational constant is:
$\Rightarrow g = \dfrac{{G{m_e}}}{{{r_e}^2}}$ … (1)
G= gravitational constant
M= mass of the earth = 10x mass of mars
R= radius of the earth
Acceleration due to gravity in terms of gravitational constant on mars is:
 $\Rightarrow g' = \dfrac{{G{m_m}}}{{{r_m}^2}}$ … (2)
 $\Rightarrow {m_m}$ = mass of mars
 $\Rightarrow {r_m}$ = radius of mars
Dividing 2 by 1
 $\Rightarrow \dfrac{{g'}}{g} = \dfrac{{\dfrac{{G{m_m}}}{{{r_m}^2}}}}{{\dfrac{{G{m_e}}}{{{r_e}^2}}}}$
 $\Rightarrow \dfrac{{g'}}{g} = \dfrac{{{m_m}{r_e}^2}}{{{r_m}^2{m_e}}}$
 $\Rightarrow \dfrac{{g'}}{g} = \dfrac{{{m_m}{{6400}^2}}}{{{{3200}^2}10{m_m}}}$
 $\Rightarrow \dfrac{{g'}}{g} = \dfrac{{{2^2}}}{{10}}$
Therefore, the value of acceleration due to gravity on mars is: 0.4g
Mass of an object weighing 200N on earth is =200/g
$\Rightarrow M= \dfrac{{200}}{g}$
Weight of the object having mass of $\dfrac{{200}}{g}$ on Mars would be:
$\Rightarrow Mg’ = \dfrac{{200g'}}{g}$
$\Rightarrow 200 \times 0.4 = 80 N$
Therefore, correct option is (A).

Note
The acceleration due to gravity is not the same at every point on earth. It differs in its value by a small amount at the equator when compared at the poles. The acceleration due to gravity changes due the shape of earth. It also varies with height, depth and also due to rotation.