Question

How much work is required to be done on a ball of mass $50g$ to give it a momentum of $600gcm{s}^{-1}$.

Answer 1

Given data:

Mass $m=50g$

We know that $1kg=1000g$,therefore $50g=\frac{50}{1000}kg\Rightarrow \frac{1}{20}kg$

momentum $p=600gcm{s}^{-1}$

We know that $1kg=1000g$ and $1m=100cm$,therefore

$$\begin{gathered} 600gcm{s}^{-1}=\frac{600}{1000\times 100}kgm{s}^{-1} \\ \Rightarrow \frac{6}{1000}kgm{s}^{-1} \end{gathered}$$

Calculation of work done:

Here the work done is equal to kinetic energy.

We know the formula for kinetic energy in terms of momentum, $KE=\frac{p^2}{2m}$,where $p$ is momentum, $KE$ is kinetic energy and $m$ is mass

$KE=\frac{{\left(\frac{6}{1000}\right)}^2}{2\left({\displaystyle \frac{1}{20}}\right)}$

$=\frac{{(0.006)}^2}{\left({\displaystyle \frac{1}{10}}\right)}$

$=\frac{0.000036}{0.1}$

$=0.0000036J\Rightarrow 3.6\times {10}^{-6}J$

Hence work is required to be done on a ball of mass $50g$ to give it a momentum of $600gcm{s}^{-1}$ is $3.6\times {10}^{-6}J$.