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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Physics
Chapter
Center of Mass, Momentum and Collision

NTA Abhyas 2020 · Physics · Center of Mass, Momentum and Collision

An isolated particle of mass m is moving in the horizontal plane...

An isolated particle of mass mm is moving in the horizontal plane (x,y)\left(x, y\right) along the xx-axis, at a certain height above the ground. It suddenly explodes into two fragments of masses m4and3m4\dfrac{m}{4} and \dfrac{3m}{4}.~An instant later, the smaller fragment is at y=+15cmy = + 15cm. The larger fragment at this instant is at

Options

  1. Ay=−5cmy = - 5cm
  2. By=+20cmy = + 20cm
  3. Cy=+5cmy = + 5cm
  4. Dy=−20cmy = - 20cm

Correct answer

A. y=−5cmy = - 5cm

Step-by-step solution

Before the explosion, the particle was moving along xx-axis i.e., it has no yy-component of velocity. Therefore, the centre of mass will not move in yy-direction or we can say ycm=0{y}_{cm} = 0.

Now, ycm=m1y1+m2y2m1+m2{y}_{cm} = \dfrac{{m}_{1}{y}_{1} + {m}_{2}{y}_{2}}{{m}_{1} + {m}_{2}}

Therefore, 0=(m/4)(+15)+(3m/4)(y)(m/4+3m/4)0 = \left(m / 4\right) \left(+15\right) + \left(3m / 4\right)\left(y\right)\left(m / 4 + 3m / 4\right)

or, y=−5cmy = - 5\text{cm}
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