First slide

Kinetic energy

Question

Which of the following statement(s) is/are correct?
I. If momentum of a body increases by 50%, its kinetic energy will increase by 125%.
II. Kinetic energy is proportional to square of velocity.

Easy

A

Only I
B

Only II
C

Both I and II
D

Neither I nor II

Solution

As momentum of a body increases by 50% of its initial momentum, $p_{2} = p_{1} + 5 q % of p_{1} = \frac{3}{2} p_{1}$
$∴ v_{2} = \frac{3}{2} v_{1}$
$As K \propto v^{2}, so K_{2} = \frac{9}{4} K_{1}$
Increase in KE $= \frac{K_{2} - K_{1}}{K_{1}} \times 100 = \frac{\frac{9}{4} K_{1} - K_{1}}{K_{1}} \times 100 = 125 %$

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