A bullet of m ass 10 g m oving horizontal w ith a velocity of 400 `ms^(-1)` strikes a w ood block of m a ss 2 kg w h ic h is s u s p e n d e d by lig h t inex ten sib le strin g of length 5 m. As resu lt the c e n tre of gravity of th e block fo und to rise a v ertical distan ce of 10 cm . The sp eed of the bullet after it em erges on horizontally from the block will b e ......

Options

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

Answer

A

Explanation

Momentum convertational rule
`(10)/( 1000) xx 400 + 2xx 0 = 2 xx v_(1) + (10)/( 1000) xx v_(2)`
Using work energy rule
Mgh `=(1)/(2) Mv_(1) 2`
`2 xx 10 xx 0.1 = (1)/(2) xx 2 xx v_(1)^(2)`
Using equation (1)
`v_(1) = 1.40 m//s`
`4 =2 xx 1.40 + 0.01 v_(2)`
`4-2.80 = 0 .01 v_(2)`
`(1.20)/( 0.01) =v_(2)`
`v_(2) = 120 ms^(-1)`