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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

200 J

250 J

150 J

answer is A.

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Detailed Solution

The kinetic energy of an object of mass m moving with a velocity of

5 m s^{- 1}

25 J

.The kinetic energy of an object will be

100 J

.
Given data in the problem,
Initial velocity,

u_{1} = 5 m s^{- 1}

Kinetic energy,

E_{k_{1}} = 25 J

So,

\Rightarrow E_{k_{1}} = \frac{1}{2} m u_{1}^{2}

When the velocity of the object is doubled then,

\Rightarrow u_{2} = 2 u_{1}

And due to this new kinetic energy will be

\Rightarrow E_{k_{2}} = \frac{1}{2} m {(2 u_{1})}^{2}

{\Rightarrow E}_{k_{2}} = 4 \times \frac{1}{2} m u_{1}^{2}

{\Rightarrow E}_{k_{2}} = 4 \times E_{k_{1}}

{\Rightarrow E}_{k_{2}} = 4 \times 25

{\Rightarrow E}_{k_{2}} = 100 J

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