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. 5 cm
• C. 2.5 cm
• D. 1.25 cm

Answer 1

The correct option is D

1.25 cm

Initially mass 10 gm moves with velocity 100 cm/s

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

$10000{=}^{20\times v_{sys},v_{sys}==50cm/s}$

If system rises upto height h then

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