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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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