Two bodies of equal masses move with uniform velocities $v$ and $3 v$ respectively. Find the ratio of their kinetic energies.

Open in App

Solution

Step 1: Given Data
Mass of 2 bodies = $m$
Velocity of body 1 (v₁) = $v$
The velocity of body 2 (v₂) = $3 v$
Step 2: Formula used
$K i n e t i c E n e r g y (K . E) = \frac{1}{2} m v^{2}$ , where $m$ is mass and $v$ is velocity.
Step 3: Finding the ratio of kinetic energies of 2 bodies
The kinetic energy of body 1, $K E_{1} = \frac{1}{2} m v^{2}$
The kinetic energy of body 2, $K E_{2} = \frac{1}{2} m {(3 v)}^{2}$
$\frac{K E_{1}}{K E_{2}} = \frac{\frac{1}{2} m v^{2}}{\frac{1}{2} m (9 v^{2})} \frac{K E_{1}}{K E_{2}} = \frac{1}{9}$
Hence, the ratio of the kinetic energies is given by $K E_{1} : K E_{2} = 1 : 9$

Suggest Corrections

Similar questions

two bodies of equal masses move with uniform velocities V and 3V respwctively.find the ratio of their kinetic energies

Two bodies of equal masses move with uniform velocities v and 3v respectively.Find the ratio of their kinetic energies.

Join BYJU'S Learning Program