Question

A bullet of mass 10g travels horizontally with speed `100m//s` and is absorbed by a wooden block of mass 900 g suspended by a string. Find the vertical height through which the block rises. Given `g=10m//s^(2)`

Answer 1

Here `m=10g=10^(2)kg.`
`u_(1)=100m//s, M=900 g=9xx10^(-1)kg`
`u_(2)=0, h=? g=10m//s^(2)`
If v is velocity of combination (bullet in block ), then from conservation of linear momentum,
`(m+M)v=m u_(1)+M u_(2)`
`=10^(-2)xx10^(2)+9xx10^(-1)xx0`
`(10^(-2)+9xx10^(-1))v=1, v=1m//s`
From `(m+M)gh=(1)/(2)(m+M)v^(2)`
`h=(v^(2))/(2g)==(1xx1)/(2xx10)m=5cm.`