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


A
Zero
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B
5cm
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C
2.5cm
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D
1.25cm
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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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