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))`

Options

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

Answer

D

Explanation

Initially mass 10gm moves with velocity 100 cm/s
`therefore` Initial momentum `=10 xx 100 = 1000 (gm xx m)/(sec)`
After collision system moves with velocity `v_(sys)`. Then
Final momentum `=(10 + 10) xx v_(sys)`
By applying the conservation of momentum
`10000= 20 xx v_(sys) rArr v_(sys)= 50 cm//s`
If system rises upto height h then `h= (v_(sys)^(2))/(2g)= (50 xx 50)/(2 xx 1000) = (2.5)/(2)= 1.25cm`