Question

8. If the momentum of a body is increased by 50%, then what will be the percentage increase in the kinetic energy of the body? [Central Schools 10] (Ans. 125%

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Answer 1

Answer:

Explanation:

The linear momentum of a body is given by:

 p=mv

And its kinetic energy is given by:

 E=12mv2

Dividing/multiplying the kinetic energy by mass of the body we get:

 E=12mm2v2

As we know that mv is called the linear momentum of the body, so we get:

 E=12mp2

When the momentum is increased by 50% , its new value becomes : p+0.5p=32p

Therefore, the new kinetic energy becomes,

 EN=12m(32p)2EN=9p22m×4EN=9p28m

Therefore the change in kinetic energy becomes:

 KE=9p28m−p22mKE=94E−EKE=54E

Therefore this means that there will be 125% increase in the KE of the body. So the correct answer is option (C).

Note

This formula relating the KE of the body with its momentum is very useful and widely used. So it is recommended that the student learns this formula. This formula in rotational mechanics is written as: KE=12IL2

Where KE is the rotational kinetic energy,

I in the moment of inertia of the body and,

L is the angular momentum of the body.

Answer 2

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