Work Energy And Power Ques 45
45. Two particles $A$ and $B$, move with constant velocities $ \vec{v} _1$ and $ \vec{v} _2$. At the initial moment their position vectors are $ \vec{r} _1$ and $ \vec{r} _2$ respectively. The condition for particles $A$ and $B$ for their collision is:
[2015 RS]
(a) $ \vec{r} _1 \cdot \vec{v} _1= \vec{r} _2 \cdot \vec{v} _2$
(b) $ \vec{r} _1 \times \vec{v} _1= \vec{r} _2 \times \vec{v} _2$
(c) $ \vec{r} _1- \vec{r} _2= \vec{v} _1 \Delta t- \vec{v} _2 \Delta t$
(d) $\frac{ \vec{r} _1- \vec{r} _2}{| \vec{r} _1- \vec{r} _2|}=\frac{ \vec{v} _1- \vec{v} _2}{| \vec{v} _1- \vec{v} _2|}$
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Answer:
Correct Answer: 45.(d)
Solution:
- (d) For collision $ \vec{V} _{B / A}$ should be along the line of action of the impulse
$ B \to A(\overrightarrow{{}r} _{A / B}) $
So, $\frac{ \vec{V} _2- \vec{V} _1}{|\vec{V}_2-\vec{V}_1|}=\frac{ \vec{r} _1- \vec{r} _2}{|\vec{r}_1-\vec{r}_2|}$
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