Physics - W.E.P. Question with Solution | TestHub

Mass of bullet $=m_1=m$ Initial speed of bullet $=u_1=v$ Mass of block $=m_2=M$ Initial speed of block $=u_2=0$ Let the common velocity of the bodies after collision $=V$ According to conservation of linear momentum $$\begin{array}{rl}m\times v+M\times 0& =(m+M)V\\ V& =\frac{mv}{(m+M)}\end{array}$$ : Heat generated = loss in $\mathrm{KE}$ $=$ Initial KE - Final KE $=\frac{1}{2}m{v}^2-\frac{1}{2}(m+M)v^2$ $=\frac{1}{2}m{v}^2-\frac{1}{2}(m+M){\left(\frac{mv}{m+M}\right)}^2$ $=\frac{1}{2}m{v}^2-\frac{1}{2}\frac{m^2{v}^2}{(m+M)}$ $=\frac{1}{2}m{v}^2\left(1-\frac{m}{m+M}\right)$ $=\frac{1}{2}m{v}^2\left(\frac{m+M-m}{m+M}\right)$ $=\frac{1}{2}\frac{mM}{(m+M)}{v}^2$