If the linear momentum is increased by 50 %, then kinetic energy will increase by

Question

If the linear momentum is increased by 50 %, then kinetic energy will increase by (A) 50 % (B) 100 % (C) 125 % (D) 25 %

Tardigrade Admin · Accepted Answer

Kinetic energy of the body, K=(p2/2 m) Since, the mass remains constant ∴ K propto p2 (K2/K1)=(p22/p12)=[(150/100)]2=(9/4) 100[(K2/K1)-1]=((9/4)-1) × 100=125 %

Q. If the linear momentum is increased by $50%$ , then kinetic energy will increase by

$50%$

$100%$

$125%$

$25%$

Kinetic energy of the body, $K = \frac{p ^{2}}{2 m}$
Since, the mass remains constant
$∴ K \propto p^{2}$
$\frac{K _{2}}{K _{1}} = \frac{p _{2}^{2}}{p _{1}^{2}} = [\frac{150}{100}]^{2} = \frac{9}{4}$
$100 [\frac{K _{2}}{K _{1}} - 1] = (\frac{9}{4} - 1) \times 100 = 125%$

Q. If the linear momentum is increased by 50%, then kinetic energy will increase by

50%

100%

125%

25%