Question

What will be the kinetic energy of a body when its mass is made four times and the velocity is doubled?

Answer 1

Step 1: Given data

$$\begin{gathered} Initialmass=m\left(say\right), \\ Initialvelocity=v\left(say\right), \\ Finalmass=4m, \\ Finalvelocity=2v \end{gathered}$$

To find the new kinetic energy.

Step 2: Formula used

The kinetic energy of an object of mass $m$and speed $v$ is given by,

$K.E=\frac{1}{2}m{v}^2$

Step 3: Calculation

$$\begin{gathered} Initialkineticenergy\left(K\right)=\frac{1}{2}m{v}^2 \\ Finalkineticenergy=\frac{1}{2}\times \left(4m\right)\times {\left(2v\right)}^2 \\ =\frac{1}{2}\times 4m\times 4v^2 \\ =16\times \frac{1}{2}m{v}^2 \\ =16K \end{gathered}$$

Hence, the kinetic energy will be 16 times the initial kinetic energy.