A shell of mass `200g` is ejected from a gun of mass `4 kg` by an explosion that generate `1.05 kJ` of energy. The initial velocity of the shell is

Options

A. `40 ms^(-1)`
B. `120 ms^(-1)`
C. `100 ms^(-1)`
D. `80 ms^(-1)`

Answer

`(3)`

Explanation

`mv = Mv. Rightarrow v. = (m/M)v` Total K.E of the bullet and gun =` 1/2 mv^(2) + 1/2 Mv^(2)`
`Total K.E = 1/2mv^(2) + 1/2M.(m^(2))/(M^(2))v^(2)`
Total K.E = `1/2 mv^(2) {1 + m/M}`
` = {1/2 xx 0.2}{1+0.2/4)}v^(2) = xx 1000J `
`Rightarrow v^(2) = (4 xx 1.05 xx1000)/(0.1 xx4.2) = 100^(2),
`therefore v= 100 ms^(-1)`