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4.1 , newtons laws of motion — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics4.1 , newtons laws of motion1 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
  • ✓
    $10\sqrt 2 \,m/second$ and $135°$ from either
  • B
    $10\sqrt 2 \,m/second$ and $45°$ from either
  • C
    $\frac{{10}}{{\sqrt 2 }}\,m/second$ and $135°$ from either
  • D
    $\frac{{10}}{{\sqrt 2 }}\,m/second$ and $45°$ from either
✓

Answer

Correct option: A.
$10\sqrt 2 \,m/second$ and $135°$ from either
a
(a)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 $P\sqrt 2 = mv\sqrt 2 = m30\sqrt 2 $
Let the velocity of mass $3m$ is $V$. So $3mV = 30m\sqrt 2 $
 $V = 10\sqrt 2 $ and angle $135°$ from either.
(as it is clear from the figure)

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