Two bodies A and B of masses $1$ and $4$ kg respectively have equal linear momentum. The ratio of their kinetic energies is?

1 : 4

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1 : 2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

4 : 1

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

1 : 16

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $4 : 1$
Kinetic energy is given as $E = \frac{1}{2} m v^{2}$
Momentum is given as $P = m v$
From the above two equations it can be written as $E = \frac{1}{2 m} P^{2} ⟹ P = \sqrt{2 m E}$
$\frac{P_{1}}{P_{2}} = \sqrt{\frac{2 m_{1} E_{1}}{2 m_{2} E_{2}}}$
$1 = \sqrt{\frac{E_{1}}{4 E_{2}}}$
$⟹ 4 = \frac{E_{1}}{E_{2}}$
$E_{1} ‘ : E_{2} = 4 : 1$

Suggest Corrections

Similar questions

1 k g

4 k g

^{'} m^{'}

^{'} 4 m^{'}

2 : 1

There are two bodies X and Y with equal kinetic energy but different masses m and 4m respectively. The ratio of their linear momentum is-

3 k g

1 k g

Join BYJU'S Learning Program