A bullet of mass `10g` moving horizontally with a velocity of `400 ms^(-1)` strikes a wooden block of mass `2 kg` which is suspended by a light in-extensible string of length `5m`. As a result, the center of gravity of the block is found to rise a vertical distance of `10cm` . The speed of the bullet after it emerges out horizontally from the block will be

Options

A. `120 ms^(-1)`
B. `160 ms^(-1)`
C. `100 ms^(-1)`
D. `80 ms^(-1)`

Answer

A

Explanation

`(10)/(1000) xx 400 + 0 = 2 xx v_(1) + (10)/(1000) xxv_(2)`
`implies 4 = 2v_(1) + 0.1 v_(2)` …(i)
Appliying work energy therom for block
`W = Delta KE`
` implies 2 xx 10 xx 0.1 = (1)/(2) xx 2 xx v_(1)^(2)`
`v_(1) = sqrt2 = 1.4 m//s`
Putting the value of `v_(1)` in equation (1).
`4 = 2 xx 1.4 = 0.01 v_(2)`
`implies v_(2) = 120 m//s`