A shell of mass 200, gm is ejected from a gun | vedclass

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Question

$\begin{array}{l}
mv = Mv'\, \Rightarrow \,v' = \left( {\frac{m}{M}} ight)v\
Total\,K.E.\,of\,the\,bullet\,and\,gun\
\,\,\,\,\,\,\,\,\,

Vedclass · Accepted Answer

$100$

Vedclass · Answer

$\begin{array}{l}
mv = Mv'\, \Rightarrow \,v' = \left( {\frac{m}{M}} ight)v\
Total\,K.E.\,of\,the\,bullet\,and\,gun\
\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{1}{2}m{v^2} + \frac{1}{2}M{v^2}\
Total\,K.E. = \frac{1}{2}m{v^2} + \frac{1}{2}M.\frac{{{m^2}}}{{{M^2}}}{v^2}
\end{array}$

$\begin{array}{l}
Total\,K.E. = \frac{1}{2}m{v^2}\left\{ {1 + \frac{m}{M}} ight\}\
 = \left\{ {\frac{1}{2} 	imes 0.2} ight\}\left\{ {1 + \frac{{0.2}}{4}} ight\}{v^2} = 1.05 	imes 1000\,J\
 \Rightarrow \,\,\,\,{v^2} = \frac{{4 	imes 1.05 	imes 1000}}{{0.1 	imes 4.2}} = {100^2}\
	herefore \,\,\,\,\,v = 100m{s^{ - 1}}
\end{array}$

A shell of mass $200\, gm$ is ejected from a gun of mass $4\, kg$ by an explosion that generates $1.05\, kJ$ of energy. The initial velocity of the shell is .............. $\mathrm{ms}^{-1}$

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