First slide

Kinetic energy

Question

Two bodies of different masses are moving with same kinetic energy. Then, the ratio of their momenta is equal to the ratio of their [Kerala CEE 2015)

Moderate

A

masses
B

square of masses
C

square root of masses
D

cube root of masses

Solution

Let the kinetic energy is K and masses of bodies are m₁ and m₂.
For first body, $p_{1} = \sqrt{2 m_{1} K}$
$∴ p_{1}^{2} = 2 m_{1} K$ …(i)
Similarly, for second body, $p_{2}^{2} = 2 m_{2} K$ …(ii)
Dividing Eq. (i) by Eq. (ii), we get
$\frac{p_{1}^{2}}{p_{2}^{2}} = \frac{2 m_{1} K}{2 m_{2} K}, \frac{p_{1}}{p_{2}} = \sqrt{\frac{m_{1}}{m_{2}}}$
$\Rightarrow \frac{p_{1}}{p_{2}} = square root of masses.$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App