SATHEE: Work Energy and Power - Result Question 47

Work Energy and Power - Result Question 47

50. 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) ${\vec{r}}_{1} \times {\vec{v}}_{1} = {\vec{r}}_{2} \times {\vec{v}}_{2}$

(d) $\frac{{\vec{r}}_{1} - {\vec{r}}_{2}}{| {\vec{r}}_{1} - {\vec{r}}_{2} |} = \frac{{\vec{v}}_{2} - {\vec{v}}_{1}}{| {\vec{v}}_{2} - {\vec{v}}_{1} |}$

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Answer:

Correct Answer: 50. (d)

Solution:

(d) For collision ${\vec{V}}_{B / A}$ should be along

$B \to A ({\vec{r}}_{A / B})$

So, $\frac{{\vec{V}}_{2} - {\vec{V}}_{1}}{| V_{2} - V_{1} |} = \frac{{\vec{r}}_{1} - {\vec{r}}_{2}}{| r_{1} - r_{2} |}$

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Work Energy and Power - Result Question 47

50. Two particles A and B, move with constant velocities v→1 and v→2. At the initial moment their position vectors are r→1 and r→2 respectively. The condition for particles A and B for their collision is:

Answer:

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50. 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: