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 reached by the system now is $(g=10m/s^2)$

• A. $Zero$
• B. $5cm$
• C. $2.5cm$
• D. $1.25cm$

Answer 1

Answer: (D)

$1.25cm$

Initially mass 10 gm moves with velocity $100cm/s$

$\therefore$ Initial momentum = $10\times 100=1000\frac{gm\times m}{sec}$

After collision system moves with velocity $v_{sys}$ then

Final momentum = $(10+10)\times v_{sys}$

By applying the conservation of momentum

$10000=20\times v_{sys}\Rightarrow V_{sys}=50cm/s$

If system rises up to height h then

$h=\frac{v_{sys}^2}{2g}=\frac{50\times 50}{2\times 1000}=\frac{2.5}{2}=1.25cm$