# Collisions

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Question

# 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 $\left(\mathrm{g}=10\text{\hspace{0.17em}}\mathrm{m}/{\mathrm{s}}^{2}\right)$

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Solution

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

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