Question

if kinetic energy is doubled what is the change in percentage of momentum?

Answer 1

$$\begin{gathered} \text{Kinetic energy is given by}\frac{1}{2}m{v}^2 \\ \text{so if kinetic energy is doubled then energy will be}2\times \frac{1}{2}m{v}^2 \\ \text{so the new velocity will be}{v}_2=\sqrt{\frac{2{\displaystyle \frac{1}{2}}m{v}^2}{\frac{1}{2}m}}=\sqrt{2}v \\ \text{so new momentum is}{P}_2=\sqrt{2}mv \\ \text{and previous momentum was}P=mv \\ \text{so momentum will increase by}\sqrt{2}=1.42\text{times}.\text{Hence momnetum will} \\ \text{increase by 41\% .} \end{gathered}$$