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Assertion : If momentum of a body increases by $50 \%$, its kinetic energy will increase by $125 \%$.
Reason : Kinetic energy is proportional to square of velocity.
Options:
Reason : Kinetic energy is proportional to square of velocity.
Solution:
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The correct answer is:
If both assertion and reason are true and reason is the correct explanation of assertion
As, $p_2=p_1+50 \%$ of $p_1=(3 / 2) p_1$
$$
\therefore \quad v_2=(3 / 2) v_1
$$
As, kinetic energy, $K \propto v^2$
$$
\therefore K_2=\frac{9}{4} K_1
$$
Increase in $\mathrm{K} . \mathrm{E} .=\frac{\left(K_2-K_1\right) \times 100}{K_1}=125 \%$.
$$
\therefore \quad v_2=(3 / 2) v_1
$$
As, kinetic energy, $K \propto v^2$
$$
\therefore K_2=\frac{9}{4} K_1
$$
Increase in $\mathrm{K} . \mathrm{E} .=\frac{\left(K_2-K_1\right) \times 100}{K_1}=125 \%$.
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