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A dog and a horse are running at the same speed. If the weight of the horse is $10$ times that of the dog, what is the ratio of their kinetic energies?

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1 : 4

1 : 6

1 : 8

1 : 10

answer is D.

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Detailed Solution

The ratio of their kinetic energies will be

1 : 10

.
The kinetic energy of a body depends upon the mass and velocity of a body. The formula for kinetic energy

(K . E .)

can be expressed as

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

where

m

is the mass of the object and

v

is its velocity.
Also, since the velocity of the bodies are same

v_{1} = v_{2}

The weight of the horse is given as ten times that of a dog.

\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{m_{1}^{}}{m_{2}^{}}

\Rightarrow = \frac{1^{}}{10}

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