Question

A ball of mass $m$ moving with a speed $u$ undergoes a head-on elastic collision with a ball of mass $nm$ initially at rest. The fraction of the incident energy, transferred to the heavier ball is :

• A. $\frac{n}{1+n}$
• B. $\frac{n}{(1+n{)}^2}$
• C. $\frac{2n}{(1+n{)}^2}$
• D. $\frac{4n}{(1+n{)}^2}$

Answer 1

The correct option is D $\frac{4n}{(1+n{)}^2}$

$mv=m{v}_1+nm{v}_2,\left(Conservationofmeomentum\right)$
$v-0=v_2-v_{1}i.e.,v_1=v_2-v(e=1)$
$mv=-mv+m{v}_2(1+n)v_2=\frac{2v}{1+n}$
$K.E.\propto m{v}^2$
The fraction of the incident energy, transferred to the heavier ball is$=\frac{{nm\left(\frac{2v}{1+n}\right)}^2}{m{v}^2}=\frac{4n}{{(1+n)}^2}$