Question

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

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Kinetic energy $E=\frac{p^2}{2m}$ where $p=mv$

Momentum is increased by $50$ %. i.e $p^{\prime }=1.5p$

$\therefore$ $E^{\prime }=\frac{(p^{\prime }{)}^2}{2m}=\frac{(1.5p{)}^2}{2m}$

$⟹$ $E^{\prime }=2.25\frac{p^2}{2m}=2.25E$

Increase in kinetic energy $\Delta E=E^{\prime }-E=2.25E-E=1.25E$

Thus kinetic energy increases by $125$ %.

Also kinetic energy $E=\frac{1}{2}m{v}^2$ $⟹E\propto v^2$

Hence if momentum is increased, then the velocity of a body increases which further increases the kinetic energy of the body.

Thus the Assertion and the reason are correct and reason explains the assertion very well.