Question

TWO OBJECTS HAVING EQUAL MASS ARE MOVING WITH unform velocities of 2m/sand 6m/s respectivelly.colcuate the ratio of thear kinetic energies

Answer 1

Let The Mass Be=x

1st Object
_________
Velocity (v)=2 m/s
$Kinetic \: energy = \frac{1}{2} \times mass \times {velocity}^{2} \\ = \frac{1}{2} \times x \times {2}^{2} \\ = \frac{1}{2}x \times 4 \\ = 2x$
Kinetic Energy of First Object=2x

2nd Object
__________
Velocity (v)=6 m/s
$Kinetic \: energy = \frac{1}{2} \times mass \times {velocity}^{2} \\ = \frac{1}{2} \times x \times {6}^{2} \\ = \frac{1}{2} x \times 36 \\ = 18x$
Kinetic Energy of Second Object=18x

Ratio=1st KE:2nd KE
=2x:18x
$\frac{2x}{18x} \\ = \frac{1}{9}$
Ratio of KE=1:9