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The kinetic energy of an object of mass $m$ , moving with a velocity of $5 m s^{- 1}$ is $25 J$ . What will be its kinetic energy when its velocity is doubled?

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100 J

50 J

12.5 J

225 J

answer is A.

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Detailed Solution

Kinetic energy will be

100 J

when its velocity is doubled.
Given:
The kinetic energy of an object

(K . E) = 25 J

The velocity of the object

(v) = 5 m s^{- 1}

Mass of the object

= m

Formula used for kinetic energy

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

For the mass of the object

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

\Rightarrow 25 = \frac{1}{2} \times m \times 5^{2}

\Rightarrow 50 = 25 m

\Rightarrow m = 2 kg

When velocity is doubled,

\Rightarrow v = 2 \times 5 m s^{- 1}

\Rightarrow v = 10 m s^{- 1} and m = 2 kg

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

\Rightarrow K . E = \frac{1}{2} \times 2 \times 1 0^{2}

\Rightarrow K . E = 100 J

So it's kinetic energy is

100 J

when its velocity is doubled.

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