A mass of 10 gm moving with a velocity of 100 cm/s strikes a pendulum bob of mass 10 gm. The two masses stick together. The maximum height (in cm) reached by the system now is $(\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2)$

Initially mass 10 gm  moves with velocity 100 cm/s
$\therefore$ Initial momentum = 10 × 100 = $1000\frac{\mathrm{gm}\times \mathrm{m}}{\sec }$
After collision system moves with velocity v_sys.  then 
Final momentum =  $(10+10)\times {\mathrm{v}}_{\text{sys.}}$
By applying the conservation of momentum 
$10000=20\times {\mathrm{v}}_{\text{sys.}}\Rightarrow {\mathrm{v}}_{\text{sys.}}=50\mathrm{cm}\text{}/\text{}\mathrm{s}$
If system rises upto height h then 
$\mathrm{h}=\frac{{\mathrm{v}}_{\text{sys.}}^{\text{2}}}{2\mathrm{g}}=\frac{50\times 50}{2\times 1000}=\frac{2.5}{2}=1.25\mathrm{cm}$