Question

A body weighs $100kg$ on earth. Find its weight on Mars. The mass and radius of Mars are $\dfrac{1}{{10}}$ and $\dfrac{1}{2}$ of the radius of earth.

Answer 1

Recall that the force of gravity or gravitational force is a phenomenon in which all the objects in the universe that have some mass are attracted towards each other. It is an invisible force but acts on every object. It is a universal force of attraction.

Complete step by step solution:
Let the mass of object on Earth be $= m$
Let the radius of Earth be $= r$
The force of gravity on earth will be given by the formula $g = \dfrac{{Gm}}{{{r^2}}}$---(i)
But it is given that the mass of object on Mars is $= {(\dfrac{m}{{10}})_{earth}}$
Also the radius on mars will be $= {(\dfrac{r}{2})_{earth}}$
So, force of gravity for Mars can be written by the same formula,
${g_{mars}} = \dfrac{{\dfrac{{Gm}}{{10}}}}{{\dfrac{{{r^2}}}{4}}}$
$\Rightarrow {g_{mars}} = \dfrac{{4Gm}}{{10{r^2}}}$
Since the weight of objects on Mars is to be calculated and the weight of objects on Earth is given so it can be written that weight on Mars will be equal to $\dfrac{4}{{10}}$ times the weight on Earth.
$\Rightarrow$Weight on Mars = Weight on Earth$\times \dfrac{4}{{10}}$
$\Rightarrow {W_{mars}} = 100 \times \dfrac{4}{{10}}$
$\Rightarrow {W_{mars}} = 40kgwt$

Therefore, the weight of the object on Mars $= 40kgwt$.

Note: It is important to note that the force of gravity depends on two factors. It depends on the mass of the object and the distance between them. It is directly proportional to the mass whereas inversely proportional to the square of distance. This means that if the distance between the objects is large then the force of gravity acting on them will be very small. But if the distance between the objects is small then the force of gravity acting on them will be large.