Question

A ball of mass $0.2\mathrm{Kg}$ is thrown vertically upwards by applying a force by hand. If the hand moves $0.2\mathrm{m}$ while applying the force and the ball goes up to $2\mathrm{m}$ height further, find the magnitude of the force. (take, $\mathrm{g}=10\raisebox{1ex}{$\mathrm{m}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{s}}^2$}\right.$)

• A. $4\mathrm{N}$
• B. $16\mathrm{N}$
• C. $20\mathrm{N}$
• D. $22\mathrm{N}$

Answer 1

The correct option is D

$22\mathrm{N}$

Step 1: Given data

Given, mass of a ball, $\mathrm{m}=0.2\mathrm{Kg}$

Total height of a ball, $\mathrm{h}={\mathrm{h}}_1+{\mathrm{h}}_2$

Here,

$$\begin{gathered} {\mathrm{h}}_1=\mathrm{height}\mathrm{of}\mathrm{a}\mathrm{ball}\mathrm{when}\mathrm{it}\mathrm{is}\mathrm{in}\mathrm{hand}=0.2\mathrm{m} \\ {\mathrm{h}}_2=\mathrm{height}\mathrm{of}\mathrm{a}\mathrm{ball}\mathrm{after}\mathrm{releasing}\mathrm{it}\mathrm{from}\mathrm{hand}=2\mathrm{m} \end{gathered}$$

Total height attained by a ball,$\mathrm{h}=0.2+2=2.2\mathrm{m}$

Let force applied$=\mathrm{F}$

Distance for which force is applied, $\mathrm{S}=0.2\mathrm{m}$

Step 2: Calculating the magnitude of force

Now we know that work done by a force is equal to potential energy. Hence,

$$\begin{gathered} \mathrm{F}.\mathrm{S}=\mathrm{mgh} \\ \Rightarrow \mathrm{F}=\frac{\mathrm{mgh}}{\mathrm{S}} \\ \Rightarrow \mathrm{F}=\frac{0.2\times 10\times 2.2}{0.2} \\ \Rightarrow \mathrm{F}=22\mathrm{N} \end{gathered}$$

So the force applied on a ball is equal to $22\mathrm{N}$.

Hence, option(D) is correct answer.