A vessel at rest explodes into three pieces. Two pieces having eq…

MCQ

A vessel at rest explodes into three pieces. Two pieces having equal masses fly off perpendicular to one another with the same velocity 18 metre per second. The third piece has three times the mass of each of the other piece. The magnitude and direction of the velocity of the third piece will be

✓
$6 \sqrt{2} m /$ second and $135^{\circ}$ from either
B
$6 \sqrt{2} m /$ second and $45^{\circ}$ from either
C
$\frac{6}{\sqrt{2}} m /$ second and $135^{\circ}$ from either
D
$\frac{6}{\sqrt{2}} m /$ second and $45^{\circ}$ from either

✓

Answer

Correct option: A.

$6 \sqrt{2} m /$ second and $135^{\circ}$ from either

(A)
Let two pieces have equal mass m and third piece has a mass of 3 m.
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.
If two particle possess same momentum and angle between them is $90^{\circ}$ then resultant will be given by
$p \sqrt{2}= mv \sqrt{2}=18 \sqrt{2} m$.
Let the velocity of mass 3m is v. So
$3 mv =18 m \sqrt{2}$
$\therefore \quad v =6 \sqrt{2} m / s$ and angle $135^{\circ}$ from either.