Centre of Mass 3 Question 17
20. A shell is fired from a cannon with a velocity $v(m / s)$ at an angle $\theta$ with the horizontal direction. At the highest point in its path it explodes into two pieces of equal mass. One of the pieces retraces its path to the cannon and the speed $(m / s)$ of the other piece immediately after the explosion is
(a) $3 v \cos \theta$
(b) $2 v \cos \theta$
(c) $\frac{3}{2} v \cos \theta$
(d) $\sqrt{\frac{3}{2}} v \cos \theta$
(1986, 2M)
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Answer:
Correct Answer: 20. (a)
Solution:
- Let $v^{\prime}$ be the velocity of second fragment. From conservation of linear momentum,
$$ \begin{aligned} & \underset{\begin{array}{l} \text { Just before } \\ \text { explosion } \end{array}}{2 m} v \cos \theta \\ & 2 m(v \cos \theta)=m v^{\prime}-m(v \cos \theta) \\ & \therefore \quad v^{\prime}=3 v \cos \theta \end{aligned} $$
