Question

If momentum is increased by 20%, then kinetic energy increases by

• A. 0.48
• B. 0.44
• C. 0.4
• D. 0.36

Answer 1

Answer: (B)

0.44

Answer 2

The kinetic energy is given by KE = $\frac{ p^2 }{ 2 m }$ So, $\triangle KE = \frac{ 2 p \triangle p }{ 2 m } = \frac{ p \triangle p }{ m }$ $\Rightarrow \frac{ 4 KE }{ KE } = \frac{ 2 \triangle p }{ p }$ Thus, the final momentum becomes 1.2 p So, percentage change in KE = $\frac{ final \, KE - initial \, KE }{ initial \, KE } \times 100$ = $\frac{ 1.44 ( p^2 / 2 m ) - ( p^2 / 2 m ) }{ ( p^2 / 2 m ) }$ = 44%