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.

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

Tardigrade Admin · Accepted Answer

As, p2 = p1 + 50 % of p1 = (3/2) p1 ∴ v2 = (3/2) v1 As, kinetic energy, K propto v2 ∴ K2=(9/4) K1 Increase in K.E. =((K2-K1)×100/K1)=125 %.

Q. 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.

If both assertion and reason are true and reason is the correct explanation of assertion

If both assertion and reason are true but reason is not the correct explanation of assertion

If assertion is true but reason is false

If both assertion and reason are false

As, $p_{2} = p_{1} + 50%$ of $p_{1} = (3/2) p_{1}$
$∴ v_{2} = (3/2) v_{1}$
As, kinetic energy, $K \propto v_{2}$
$∴ K_{2} = \frac{9}{4} K_{1}$
Increase in K.E. $= \frac{( K _{2} - K _{1} ) \times 100}{K _{1}} = 125%.$

Q. 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.