Question

A body of mass 'm' strikes another body at rest of mass ${}^{\prime }{\frac{m}{90}}^{\prime }$. Assuming the impact to be inelastic the fraction of the initial kinetic energy transformed into heat during the contact is

Answer 1

Fraction of $K.E$ transformed into heat $=\frac{4Mm}{{(M+m)}^2}$

Here $M=m$ ; $m=\frac{m}{90}$

$\therefore$ fraction $=\frac{4m.\frac{m}{90}}{{(m+\frac{m}{90})}^2}=\frac{{4m}^2}{{\left(\frac{91m}{90}\right)}^2.90}$

$=\frac{4\times 90}{{91}^2}=\frac{360}{{\left(91\right)}^2}=\frac{360}{8281}$