Question

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

• A. 50%
• B. 100%
• C. 125%
• D. 25%

Answer 1

Answer: (C)

125%

Answer 2

Let $P _ { 1 } = P$, $P _ { 2 } = P _ { 1 } + 50 \%$ of $P _ { 1 }$ = $P _ { 1 } + \frac { P _ { 1 } } { 2 } = \frac { 3 P _ { 1 } } { 2 }$

$E \propto P ^ { 2 }$⇒ $\frac { E _ { 2 } } { E _ { 1 } } = \left( \frac { P _ { 2 } } { P _ { 1 } } \right) ^ { 2 } = \left( \frac { 3 P _ { 1 } / 2 } { P _ { 1 } } \right) ^ { 2 } = \frac { 9 } { 4 }$

⇒ $E _ { 2 } = 2.25 E$ $= E _ { 1 } + 1.25 E _ { 1 }$

∴ $E _ { 2 } = E _ { 1 } + 125 \%$ of $E _ { 1 }$

i.e. kinetic energy will increase by 125%.