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. If both assertion and reason are true and reason is the correct explanation of assertion
• B. If both assertion and reason are true but reason is not the correct explanation of assertion
• C. If assertion is true but reason is false
• D. If both assertion and reason are false

Answer 1

Answer: (A)

As, $p_2 = p_1 + 50\%$ of $p_1 = (3/2) p_1$
$\therefore \, v_2 = (3/2) v_1$
As, kinetic energy, $K \propto v_2$
$\therefore K_{2}=\frac{9}{4} K_{1}$
Increase in K.E. $=\frac{\left(K_{2}-K_{1}\right)\times100}{K_{1}}=125\%.$