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BITSAT 2023Paper 2
Exam
BITSAT
Year
2023
Paper
Paper 2
Subject
Physics
Chapter
Motion in One Dimension

BITSAT 2023 · Paper 2 · Physics · Motion in One Dimension

A passenger sitting in a train A moving at 90 km /h observes...

A passenger sitting in a train A moving at 90km/h90 \mathrm{ km} /h observes another train B moving in the opposite direction for 8s8 \mathrm{ s}. If the velocity of the train B is 54km/h54 \mathrm{ km} / \mathrm{h}, then length of train B is :

Options

  1. A80m80 \mathrm{ m}
  2. B200m200 \mathrm{ m}
  3. C120m120 \mathrm{ m}
  4. D320m320 \mathrm{ m}

Correct answer

D. 320m320 \mathrm{ m}

Step-by-step solution

Velocity of train A
(\mathrm{V}_{\mathrm{A}}=90 \frac{\mathrm{km}}{\mathrm{hr}}=90 \times \frac{5}{18}=25 \mathrm{ m}/ \mathrm{s})
Velocity of train B
(\mathrm{V}_{\mathrm{B}}=54 \frac{\mathrm{km}}{\mathrm{hr}}=54 \times \frac{5}{18}=15 \mathrm{ m}/ \mathrm{s})
Velocity of train B w.r.t. train
<br/>A=V⃗B−V⃗A<br/>=15−(−25)m/s<br/>=40m/s<br/>\begin{aligned}<br />A=\vec{V}_B & -\vec{V}_A \\<br />& =15-(-25) \mathrm{m}/ \mathrm{s}\\<br />& =40 \mathrm{ m}/ \mathrm{s}<br />\end{aligned}
Time of crossing (=\frac{\text{ length of train }}{\text{ relative velocity }})
((8)=\frac{\ell}{40})
(\ell=8 \times40=320) meter.
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