Question

If the momentum of an object is increased by 10% then its kinetic energy will increase by?

Answer 1

Step 1. Definition of momentum

It is defined as a product of mass and velocity.

Step 2. Definition of Kinetic energy

Kinetic energy is the amount of energy that an object or particle has due to its motion.

Step 3. Given data:

Final momentum = initial momentum + $\left(10\%\right)$ of initial momentum.

Step 4. Calculations:

We know Kinetic energy ${\left(KE\right)}_1$ = $\frac{p^2}{2m}$, ……..$\left(1\right)$

Where, $p$= momentum, $m$=mass of the body,

If we increase $p$ by $10\%$,

Then final $p$ = $p+\frac{p}{10}$=$\frac{11p}{10}$, Putting this value of $p$ in $\left(1\right)$, we get

${\left(KE\right)}_2$ = $\frac{{\left({\displaystyle \raisebox{1ex}{$11p$}\!\left/ \!\raisebox{-1ex}{$10$}\right.}\right)}^2}{2m}=\frac{121}{100}.\frac{p^2}{2m}=\frac{121}{100}.{\left(KE\right)}_1$

Change in kinetic energy, $∆KE={\left(KE\right)}_2-{\left(KE\right)}_1$= $={\frac{121}{100}{\left(KE\right)}_1-{\left(KE\right)}_1=\left(KE\right)}_1\left(\frac{121}{100}-1\right)=\frac{21}{100}{\left(KE\right)}_1$

So $\frac{∆KE}{{\left(KE\right)}_1}\times 100=21$

Hence kinetic energy will change by $21\%$, If momentum will increase by $10\%$.