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 $$(g = 10 m/s^2)$$

A
Zero
B
5cm
C
2.5cm
D
1.25cm

Solution

## The correct option is A $$1.25 cm$$Initially mass 10 gm moves with velocity $$100 cm/s$$$$\therefore$$ 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 $$10000 = 20 \times v_{sys} \Rightarrow V_{sys} = 50 cm/ s$$If system rises up to height  h then $$h = \dfrac { v^2_{sys} }{2g} = \dfrac { 50 \times 50}{ 2 \times 1000} = \dfrac {2.5}{2} = 1.25 cm$$Physics

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