Question

A ball of mass $m$ moving with a speed $u$ undergoes a heat-on 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

Answer: (D)

$\frac{4n}{(1+n{)}^2}$

$e=\frac{v_2-v_1}{\mu -0}$

$\mu =v_2-v_1$

$m{v}_1+nm{v}_2=mu$

$(n+1)v_2=2u$

$v_2=\left(\frac{2u}{n+1}\right)$

Fraction of K.E to body $=\frac{\frac{1}{2}\times nm\times {\left(\frac{2u}{n+1}\right)}^2}{\frac{1}{2}\times m\times u^2}$ $=\frac{4n}{(n+1{)}^2}$