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Two bodies having equal masses are moving with uniform speeds of $v$ and $2 v$ respectively. Find the ratio of their kinetic energies.

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1 : 4

3 : 4

1 : 3

3 : 2

answer is A.

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Detailed Solution

Two bodies having equal masses are moving with uniform speeds of

v

and

2 v

respectively. The ratio of their kinetic energies is

1 : 4

The kinetic energy of a body depends upon the mass

(m)

and velocity

(v)

of the body.The formula for kinetic energy

(K . E .)

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

Also, since the mass of the bodies are same

m_{1} = m_{2}

\frac{K E_{1}}{K E_{2}} = \frac{½ m v_{1}^{2}}{½ m v_{2}^{2}}

\frac{K {E_{1}}_{}}{K E_{2}} = \frac{v_{1}^{2}}{v_{2}^{2}}

\Rightarrow = \frac{1^{2}}{2^{2}}

\Rightarrow = \frac{1}{4}

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