A vessel at rest exlodes breaking it into three piecess. Two pieces having equal mass fly off prependicular to one anther with the same speed of `30m//s` . The third pieces has three times the mass of each other piece. What is the direction (w.r.t. the piece having equal masses) and magnitude of its velocity immediately after the explosion?

Options

A. `10sqrt(2) ` m/second and `135^(@)` from either
B. `10sqrt(2)` m/second and `45^(@)` from either
C. `(10)/(sqrt(2))` m/second and `135^(@)` from either
D. `(10)/(sqrt(2))` m/second and `45^(@)` from either

Answer

A

Explanation

Let two pieces are having equal mass m and third piece have a mass of 3m.

According to law of conservation of linear momentum. Since the initial momentum of the system was zero, therefore final momentum of the system must be zero i.e. the resultant of momentum of two pieces must be equal to the momentum of third piece. We know that if two particle possesses same momentum and angle in between them is `90^(@)` then resultant will be given by `Psqrt(2) = m v sqrt(2) = m 20 sqrt(2)`
Let the velocity of mass 3m is V. So `3m V = 30 m sqrt(2)`
`therefore V = 10 sqrt(2)` and angle `135^(@)` from either. (as it is clear from the figure)