Question

The momentum of a body is increased by 25%. The kinetic energy is increased by about :

• A. 25%
• B. 5%
• C. 56%
• D. 38%

Answer 1

Answer: (C)

56%

Answer 2

kinetic energy of the body is

Where p is the momentum and m is the mass of a body respectively.

$\therefore \mathrm { k } \propto \mathrm { p } ^ { 2 }$

When the momentum of a body is increased by 25%, its momentum will become

$\therefore \frac { \mathrm { k } ^ { \prime } } { \mathrm { k } } = \frac { \mathrm { p } ^ { \prime 2 } } { \mathrm { p } ^ { 2 } } = \left( \frac { 5 } { 4 } \right) ^ { 2 } = \frac { 25 } { 16 }$

Or

Percentage increase in the kinetic energy of the body

$= \frac { \mathrm { k } ^ { \prime } - \mathrm { k } ^ { \prime } } { \mathrm { k } } \times 100$

$= \frac { 9 } { 16 } \times 100 = 56 \%$