b
\(\begin{array}{l}
\,\,\,\,\,Mass\,of\,bullet,\,m = 10\,g = 0.01kg\\
Initial\,speed\,of\,bullet,\,u = 400\,m{s^{ - 1}}\\
Mass\,of\,block,\,M = 2\,kg\\
Lenght\,of\,string\,l = 5\,m\\
Speed\,of\,the\,block\,after\,collision = {v_1}\\
Speed\,of\,the\,bullet\,on\,emerging\,from\\
block,\,v = ?\\
{\rm{Using}}\,energy\,conseravtion\,principel\\
for\,the\,block,
\end{array}\)

\(\begin{array}{l}
\,\,\,\,\,\,\,\,\,\,\,{(KE + PE)_{{\mathop{\rm Re}\nolimits} ference}} = {\left( {KE + PE} \right)_h}\\
 \Rightarrow \,\frac{1}{2}Mv_1^2 = Mgh\,\,\,or,\,\,\,{v_1} = \sqrt {2gh} \\
\,\,\,\,\,{v_1} = \sqrt {2 \times 10 \times 0.1}  = \sqrt 2 \,m{s^{ - 1}}\\
{\rm{Using}}\,momentum\,conservation\,principle\\
for\,block\,and\,bullet\,system,
\end{array}\)

\(\begin{array}{l}
{\left( {M \times 0 + mu} \right)_{Before\,collision}} = {\left( {M \times {v_1} + mv} \right)_{After\,collision}}\\
 \Rightarrow \,0.01 \times 400 = 2\sqrt 2  + 0.01 \times v\\
 \Rightarrow v = \frac{{4 - 2\sqrt 2 }}{{0.01}} = 117.15\,m{s^{ - 1}} \approx 120\,m{s^{ - 1}}
\end{array}\)