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Centre of Mass, Linear Momentum, Collision — Physics STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 SciencePhysicsCentre of Mass, Linear Momentum, Collision1 Mark
Question
A shell is fired from a cannon with a velocity V at an angle $\theta$ with the horizontal direction. At the highest point in its path, it explodes into two pieces of equal masses. One of the pieces retraces its path to the cannon. The speed of the other piece immediately after the explosion is:
  1. $\text{3V}\cos\theta$
  2. $2\text{V}\cos\theta$
  3. $\frac{3}{2}\text{V}\cos\theta$
  4. $\text{V}\cos\theta$
✓

Answer

  1. $\text{3V}\cos\theta$
Explanation:
The linear momentum is conserved in horizontal direction.

Initial momentum = Final momentum
$\Rightarrow\text{mv}\cos\theta=-\frac{\text{m}}{2}\text{v}\cos\theta+\frac{\text{m}}{2}\text{v}'$
$\Rightarrow\text{v}'=\text{mv}\cos\theta$

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