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NEET 2015
Exam
NEET
Year
2015
Subject
Physics
Chapter
Motion in One Dimension

NEET 2015 · Physics · Motion in One Dimension

Two particles A and B move with constant velocities → v _ 1 and → v...

Two particles A and B move with constant velocities v→1{\overset{\to}{v}}_{1} and v→2{\overset{\to}{v}}_{2}. At the initial moment their position vectors are r→1{\overset{\to}{r}}_{1} and r→2{\overset{\to}{r}}_{2} respectively. The condition for particles A and B for their collision is:

Options

  1. A{\overset{\to}{r}}_{1} ⋅ {\overset{\to}{v}}_{1} = {\overset{\to}{r}}_{2} ⋅ {\overset{\to}{v}}_{2}
  2. Br→1×v→1=r→2×v→2{\overset{\to}{r}}_{1} \times {\overset{\to}{v}}_{1} = {\overset{\to}{r}}_{2} \times {\overset{\to}{v}}_{2}
  3. Cr→1−r→2=v→1−v→2{\overset{\to}{r}}_{1} - {\overset{\to}{r}}_{2} = {\overset{\to}{v}}_{1} - {\overset{\to}{v}}_{2}
  4. Dr→1−r→2∣r→1−r→2∣=v→2−v→1∣v→2−v→1∣\dfrac{{\overset{\to}{r}}_{1} - {\overset{\to}{r}}_{2}}{\left|{\overset{\to}{r}}_{1} - {\overset{\to}{r}}_{2}\right|} = \dfrac{{\overset{\to}{v}}_{2} - {\overset{\to}{v}}_{1}}{\left|{\overset{\to}{v}}_{2} - {\overset{\to}{v}}_{1}\right|}

Correct answer

D. r→1−r→2∣r→1−r→2∣=v→2−v→1∣v→2−v→1∣\dfrac{{\overset{\to}{r}}_{1} - {\overset{\to}{r}}_{2}}{\left|{\overset{\to}{r}}_{1} - {\overset{\to}{r}}_{2}\right|} = \dfrac{{\overset{\to}{v}}_{2} - {\overset{\to}{v}}_{1}}{\left|{\overset{\to}{v}}_{2} - {\overset{\to}{v}}_{1}\right|}

Step-by-step solution

For two particles to collide, the direction of the relative velocity of one with respect to other should be directed towards the relative position of the other particle i.e. (\frac{\vec{r}_1-\vec{r}_2}{\left|\vec{r}_1-\vec{r}_2\right|} \rightarrow) direction of relative position of 1 w.r.t. 2. & (\frac{\vec{v}_2-\vec{v}_1}{\left|\vec{v}_2-\vec{v}_1\right|} \rightarrow) direction of velocity of 2 w.r.t. 1 So for collision of A & B (\frac{\vec{r}_1-\vec{r}_2}{\left|\vec{r}_1-\vec{r}_2\right|}=\frac{\vec{v}_2-\vec{v}_1}{\left|\vec{v}_2-\vec{v}_1\right|})
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