Question

A man on a certain planet throws up a stone of $500g$ with a velocity of $10m/s$ and catches it after 8 seconds. What is the weight of the stone on the planet?

Answer 1

Hint:-Since the man is throwing stone upwards, it will come back due to the action of gravity. It is to be remembered that anything that has mass will have gravity. So whether it can be any planet, on which the stone is thrown, but it will have some value of gravity.

Complete step-by-step solution:
Step I:
The amount of time that any object spends in the air is known as its time of flight. Let the acceleration due to gravity on the planet be ‘$g$'. Then time of flight is given by the formula,
$T = \dfrac{{2u}}{g}$
Where $T$ is the time = 8seconds
And $u$ is the initial velocity$ = 10m/s$
Step II:
Substituting the given values in the formula and evaluating value of g
$8 = \dfrac{{2 \times 10}}{g}$
$g = \dfrac{{20}}{8}m{s^{ - 2}}$
Step III:
Weight of an object is the force acting on the object due to gravity. It’s formula is given as the product of the mass of the body and acceleration. Here the acceleration is due to gravity. So formula becomes,
$Weight = mg$
$ = \dfrac{{500}}{{1000}} \times \dfrac{{20}}{8}$
$ = \dfrac{{10}}{8}N$
Step IV:
Therefore, the weight of the stone on the planet will be $\dfrac{{10}}{8}N$.

Note:- It is to be noted that gravitational force is the force of attraction. It is the type of force that brings two bodies close to each other. The force of gravity varies according to the mass of the object. If the object is heavier, then it will have more force of gravity. But if the object has less weight then it will have a small force of gravity. Hence, Everything in the universe has gravity.