Question

A man on a certain planet throws a body of mass $500gm$ with a velocity of $10m/s$ and catches it after $8$ seconds. Find the weight of the body on the planet.

Answer 1

Hint: In order to answer this question, to find the weight of the given body on the planet, we will first calculate the acceleration due to gravity with the help of the given initial velocity of the body and the time given of catching. And after that we can find the weight, as mass is given.

Complete step by step answer:
Let the acceleration due to gravity of the planet is $g$.
So, we have the formula in which it show the relation of time and acceleration:
$\therefore t={\displaystyle \frac{2u}{g}}$
Here, $t$ is the time.
$u$ is the initial velocity.
and $g$ is the acceleration due to gravity of the planet.
$$\begin{gathered} \Rightarrow 8={\displaystyle \frac{2\times 10}{g}} \\ \Rightarrow g={\displaystyle \frac{20}{8}}m.s^{-2} \end{gathered}$$
Now, we can find the weight of the body by applying the formula which relate the weight, mass and acceleration due to gravity:
$\therefore Weightofthebody=m.g={\displaystyle \frac{500}{1000}}\times {\displaystyle \frac{20}{8}}={\displaystyle \frac{10}{8}}N$
Hence, the required weight of the body on the planet is ${\displaystyle \frac{10}{8}}N$ or $1.25N$.

Note: Now, a question arises here that why do we use Kilograms to measure weight instead of Newton in certain conditions? So, mass is the same everywhere on earth, weight is not - it can vary as much as $$0.7\mathrm{\%}$$ from the North Pole (heavy) to the mountains of Peru (light). This is in part caused by the rotation of the earth, and in part by the fact that the earth's surface is not (quite) a sphere. Or in simplest words, on the other planets except earth, weight will be often measured in the mass due to the different gravitational forces.