Centre of Mass 3 Question 21
24. The speed of the block at point $B$ immediately after it strikes the second incline is
(a) $\sqrt{60} m / s$
(b) $\sqrt{45} m / s$
(c) $\sqrt{30} m / s$
(d) $\sqrt{15} m / s$
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Answer:
Correct Answer: 24. (b)
Solution:
- Between $A$ and $B$, height fallen by block
$$ h _1=\sqrt{3} \tan 60^{\circ}=3 m $$
$\therefore$ Speed of block just before striking the second incline,
$$ v _1=\sqrt{2 g h _1}=\sqrt{2 \times 10 \times 3}=\sqrt{60} ms^{-1} $$
In perfectly inelastic collision, component of $v _1$ perpendicular to $B C$ will become zero, while component of $v _1$ parallel to $B C$ will remain unchanged.
$\therefore$ Speed of block $B$ immediately after it strikes the second incline is,
$v _2=$ component of $v _1$ along $B C$
$$ \begin{aligned} & =v _1 \cos 30^{\circ}=(\sqrt{60}) \frac{\sqrt{3}}{2} \\ & =\sqrt{45} ms^{-1} \end{aligned} $$
