Question:
An isolated particle of mass $m$ is moving in a horizontal plane$ (x-y)$ along the $x$-axis, at a certain height above the ground. It suddenly explodes into two fragments of masses $m/4$ and $3m/4$ . An instant later, the smaller fragment is at $y = +15 \,cm$. The larger fragment at this instant is at
An isolated particle of mass $m$ is moving in a horizontal plane$ (x-y)$ along the $x$-axis, at a certain height above the ground. It suddenly explodes into two fragments of masses $m/4$ and $3m/4$ . An instant later, the smaller fragment is at $y = +15 \,cm$. The larger fragment at this instant is at
Updated On: Jul 27, 2022
- $y=-5\,cm$
- $y=20\,cm$
- $y=+5\,cm$
- $y= - 20\,cm$
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The Correct Option is A
Solution and Explanation
Since there is no external force acting on the particle, hence
$y_{CM}=\frac{m_{1}y_{1}+m_{2}y_{2}}{m_{1}+m_{2}}=0$,
$\therefore \left(\frac{m}{4}\right)\times\left(+15\right)+\left(\frac{3m}{4}\right)\left(y_{2}\right)=0$
$\Rightarrow y_{2}=-5\, cm$
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Concepts Used:
System of Particles and Rotational Motion
- The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
- The distance between the pair of particles in such a body does not replace or alter. Rotational motion can be described as the motion of a rigid body originates in such a manner that all of its particles move in a circle about an axis with a common angular velocity.
- The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.