Two objects having equal masses are moving with uniform velocities of $2\ m/s$ and $6\ m/s$ respectively. Calculate the ratio of their kinetic energies.

Let $m$ be the mass of each object. As given,

Velocity of first object $v_1=2\ m/s$

Velocity of second object $v_2=6\ m/s$

Therefore, Kinetic energy of first object $K_1=\frac{1}{2}mv_1^2$

$=\frac{1}{2}m(2)^2$

$=2m\ Joule$

Similarly, the kinetic energy of the second object $K_2=\frac{1}{2}mv_2^2$

$=\frac{1}{2}m(6)^2$

$=18m\ Joule$

Therefore, $\frac{K_1}{K_2}=\frac{2m}{18m}$

Or $K_1:K_2=1:9$

Therefore, the ratio of the kinetic energies is $1:9$.

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Updated on: 10-Oct-2022

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