A shell of mass 5M, acted upon by no external force and initially at rest, bursts into three fragments of masses M, 2M and 2M respectively. The first two fragments move in opposite directions with velocities of magnitude 2v and v respectively. The third fragment will

Options

A. Move with a velocity V in a direction perpendicular to the other two
B. Move with a velocity 2V in the direction of velocity of the first fragment
C. Be at rest
D. Move with a velocity V in the direction of velocity of the second fragment

Answer

C

Explanation

`[(m_(1)v_(1))hat(i) - (m_(2)v_(2))hat(j)] =m_(3)v_(3)`
`rArr (M xx 2v)hat(i) - (2M xx v) hat(i) = m_(3)v_(3)`
`m_(3) v_(3) = 0 rArr v_(3) = 0`