Question

The kinetic energy of a body decreases by $19$% what is the percentage decrease in momentum:

• A. $20$ %
• B. $15$ %
• C. $10$ %
• D. $5$ %

Answer 1

The correct option is C $10$ %

Let percentage decrease in momentum $=X$ %

Decrease in momentum $m{v}_1-m{v}_2=m(v_1-v_2)=\left(0.0X\right)m{v}_1$

we can write it like this - $v_2=(1-0.0X)v_1$ ....(1)

Change in $KE$ - $\frac{1}{2}m(v_1^2-v_2^2)=0.19\frac{1}{2}m{v}_1^2$

$⟹v_2^2=0.81v_1^2$

By equation (1) we get $(1-0.0X{)}^2=0.81$

$⟹X=10$