Question

If the K.E. of a body is increased by 300%, its momentum will increase by

• A. 100%
• B. 150%
• C. $\sqrt { 300 } \%$
• D. 175%

Answer 1

Answer: (A)

100%

Answer 2

Let initial kinetic energy, $E _ { 1 } = E$

Final kinetic energy, $E _ { 2 } = E + 300 \%$ of E = 4E

As $P \propto \sqrt { E }$⇒ $\frac { P _ { 2 } } { P _ { 1 } } = \sqrt { \frac { E _ { 2 } } { E _ { 1 } } } = \sqrt { \frac { 4 E } { E } } = 2$ ⇒ $P _ { 2 } = 2 P _ { 1 }$

⇒ $P _ { 2 } = P _ { 1 } + 100 \%$ of $P _ { 1 }$

i.e. Momentum will increase by 100%.