Question

Two bodie of equal masses move with a uniform velocities v and 3v respectively.Find the ratio of their kinetic energyies

Answer 1

K1/K2=m1 v^2/m2 (3v)^2
=1/9 as m1=m2

Ratio is 1:9

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Answer 2

$\bigstar$  Question  $\bigstar$

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

$\star$  Answer  $\star$

1:9

$\bigstar$  Step By Step Explanation $\bigstar$

Body 1

Mass = 'm'

Velocity = 'v'

E$\mathsf{_k}}$ = $\frac{1}{2}$ mv²

Body 2

Mass = 'm'

Velocity = '3v'

E$\mathsf{_k}}$ = $\frac{1}{2}$ m[3v]²

$\varphi$  Dividing both Energies to get the ratio of Kinetic Energies  $\varphi$

= $\mathsf{\frac{\frac{1}{2}m \ v^{2} }{\frac{1}{2} m \ [3v]^{2} }}}$

1/2 gets cancelled, 'm' gets cancelled.

= $\mathsf{\frac{v^{2}}{9v^{2}}}}$

v² gets cancelled on both sides.

= $\mathsf{\frac{1}{9}}$

= 1 : 9

Hence, the ratio of the two bodies Kinetic Energy is 1 : 9