Question

If the kinetic energy of a body increases by $0.1\%$, the percent increase of its momentum will be ......

• A. $0.05\%$
• B. $0.1\%$
• C. $1.0\%$
• D. $10\%$

Answer 1

The correct option is A $0.05\%$

It is known that $P=mv$ and $E=\frac{1}{2}m{v}^2$

so $P=\sqrt{2mE}\therefore P\propto \sqrt{E}$
Percentage increase in $P=\frac{1}{2}$ (percentage increase in $E$ )
$=\frac{1}{2}(0.1$ %) = $0.05$ %