A body of m ass (4m) is lying x-y p lan e at rest. It su d d en ly explodes in to th re e pieces. Two pieces, each of m ass (m) m ove p erp en d icu lar to each o th er w ith equal speeds (p). The total kinetic energy g en erated due to explosion is

Options

A. `mv^(2)`
B. `3/2 mv^(2)`
C. `2mv^(2)`
D. `4 mv^(2)`

Answer

B

Explanation

As pser law of conservation of momentum
`vec( P )_(i) = vec( p)_(f )`
`0 = mv hat(I ) + mvhat(j ) + 2 mvec( v)`
`|vec(v )| = sqrt((v)/(2))^(2) + ((v)/(2))^(2)`
`=sqrt((v^(2))/(2))`
Kinetic energy `=(1)/(2) mv^(2) +(1)/(2) mv^(2) + (1)/(2) (2m). (v^(2))/( 2)`
`=mv^(2) + (1)(2) mv^(2)`
`=(3)/(2) mv^(2)`