Question

If the $KE$ of a particle becomes four times its initial value, then the new momentum is more than its initial momentum by

• A. $50$ %
• B. $100$ %
• C. $125$ %
• D. $150$ %

Answer 1

The correct option is B $100$ %

Initial $KE\left(T\right)$
$T=\frac{1}{2}m{v}^2$

$T_2=4T=\frac{1}{2}m{v}_2^2$

$2m{v}^2=\frac{1}{2}m{v}_2^2$

$v_2^2=4v^2$
i.e.
$v_2=2v$
Change in momentum is:
$2mv-mv=mv$
Which is $100$% of the initial.