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What is the ratio of kinetic energies of two bodies of equal masses moving with a uniform velocity of $v$ and $3 v$ respectively?

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1 : 2

1 : 3

1 : 9

3 : 7

answer is C.

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Detailed Solution

The ratio of kinetic energies of the given bodies is

1 : 9

.
The given velocities of two masses are

v

and

3 v

.
Let the mass of each body

= m

We know that

K . E . = \frac{1}{2} m v^{2}

So, for first body

K . E ._{1} = \frac{1}{2} m v^{2}

….(1)
For second body

K . E ._{2} = \frac{1}{2} m {(3 v)}^{2}

\Rightarrow K . E ._{2} = \frac{9}{2} m v^{2}

….(2)
Divide equation (1) by equation(2) we get,
⇒

\frac{K . E_{1}}{K . E_{2}} = \frac{\frac{1}{2} m v^{2}}{\frac{9}{2} m v^{2}}

⇒

\frac{K . E_{1}}{K . E_{2}} = \frac{\frac{1}{2}}{\frac{9}{2}}

⇒

\frac{K . E_{1}}{K . E_{2}} = \frac{1}{2} \times \frac{2}{9}

⇒

\frac{K . E_{1}}{K . E_{2}} = \frac{1}{9}

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