A bullet of mass \(10\, g\) moving horizontally with a velocity of \(400\, m s^{-1}\) strikes a wood block of mass \(2\, kg\) which is suspended by light inextensible string of length \(5\, m.\) As a result, the centre of gravity of the block found to rise a vertical distance of \(10\, cm.\) The speed of the bullet after it emerges out horizontally from the block will be ................... \(\mathrm{ms}^{-1}\)

\(\begin{array}{l}
\,\,\,\,\,Mass\,of\,bullet,\,m = 10\,g = 0.01kg\\
Initial\,speed\,of\,bullet,\,u = 400\,m{s^{ - 1}}\\
Mass\,of\,block,\,M = 2\,kg\\
Lenght\,of\,string\,l = 5\,m\\
Speed\,of\,the\,block\,after\,collision = {v_1}\\
Speed\,of\,the\,bullet\,on\,emerging\,from\\
block,\,v = ?\\
{\rm{Using}}\,energy\,conseravtion\,principel\\
for\,the\,block,
\end{array}\) \(\begin{array}{l}
\,\,\,\,\,\,\,\,\,\,\,{(KE + PE)_{{\mathop{\rm Re}\nolimits} ference}} = {\left( {KE + PE} \right)_h}\\
 \Rightarrow \,\frac{1}{2}Mv_1^2 = Mgh\,\,\,or,\,\,\,{v_1} = \sqrt {2gh} \\
\,\,\,\,\,{v_1} = \sqrt {2 \times 10 \times 0.1}  = \sqrt 2 \,m{s^{ - 1}}\\
{\rm{Using}}\,momentum\,conservation\,principle\\
for\,block\,and\,bullet\,system,
\end{array}\)