A body of mass M at rest explodes into three pieces, two of which of mass M//4 each are thrown off in perpendicular directions with velocities of `3//s` and `4m//s` respectively. The third piece will be thrown off with a velocity of

Options

A. `1.5 ms^(-1)`
B. `2 ms^(-1)`
C. `2.5 ms^(-1)`
D. `3 ms^(-1)`

Answer

C

Explanation

( c) Momentum of one piece` =(M)/(4)xx3`
Momentum of other piece`=(M)/(4)xx4`
`therfore` Resultant momentum`=sqrt((9M^(2)/(16)+M^(2))=(5M)/(4)`
The third piece should also have the same momentum. Let its velocity be v, then `(5M)/(4)=(M)/(2)xxv impliesv=(5)/(2)=2.5 ms^(-1)`