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Work, Energy, Power and Collision — JEE physics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceJEE physicsWork, Energy, Power and Collision1 Mark
MCQ
A vessel at rest explodes into three pieces. Two pieces having equal masses fly off perpendicular to one another with the same velocity 30 meter per second. The third piece has three times mass of each of other piece. The magnitude and direction of the velocity of the third piece will be
  • ✓
    $10 \sqrt{2} \mathrm{~m} / \mathrm{second}$ and $135^{\circ}$ from either
  • B
    $10 \sqrt{2} \mathrm{~m} / \mathrm{second}$ and $45^{\circ}$ from either
  • C
    $\frac{10}{\sqrt{2}} \mathrm{~m} / \mathrm{second}$ and $135^{\circ}$ from either
  • D
    $\frac{10}{\sqrt{2}} \mathrm{~m} / \mathrm{second}$ and $45^{\circ}$ from either
✓

Answer

Correct option: A.
$10 \sqrt{2} \mathrm{~m} / \mathrm{second}$ and $135^{\circ}$ from either
Let two pieces are having equal mass $m$ and third piece have a mass of $3\ m .$

According to láw 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 $90^{\circ}$ then resultant will be given by $P \sqrt{2}=m v \sqrt{2}=m 30 \sqrt{2}$
Let the velocity of mass $3 m$ is $V$. So $3 m V=30 m \sqrt{2}$
$\therefore \quad V=10 \sqrt{2}$ and angle $135^{\circ}$ from either.
(as it is clear from the figure)

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