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Motion in A Straight Line question

2023 · 13 Apr · Shift 1 · Q57
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  5. /2023 · 13 Apr · Shift 1 · Q57

Motion in A Straight Line question

2023 · 13 Apr · Shift 1 · Q57

JEE MainPhysicsMotion in A Straight LineMCQ+4 / −1
Two trains 'A' and 'B' of length 'lll' and '4l4 l4l' are travelling into a tunnel of length 'L\mathrm{L}L' in parallel tracks from opposite directions with velocities 108 km/h108 \mathrm{~km} / \mathrm{h}108 km/h and 72 km/h72 \mathrm{~km} / \mathrm{h}72 km/h, respectively. If train 'A' takes 35 s35 \mathrm{~s}35 s less time than train 'B' to cross the tunnel then. length 'LLL' of tunnel is : (Given L=60l\mathrm{L}=60 lL=60l )
  1. A
    900 m
  2. B
    1200 m
  3. C
    1800 m
  4. D
    2700 m
View written solutionFree

Correct answer: C

  1. Convert speeds into SI units

Train A: 108 km/h=108×518=30 m/s108\ \text{km/h} = 108\times \frac{5}{18} = 30\ \text{m/s}108 km/h=108×185​=30 m/s

Train B: 72 km/h=72×518=20 m/s72\ \text{km/h} = 72\times \frac{5}{18} = 20\ \text{m/s}72 km/h=72×185​=20 m/s

  1. Time taken by each train to completely cross the tunnel

To completely cross a tunnel, a train must cover: distance=length of tunnel+length of train\text{distance} = \text{length of tunnel} + \text{length of train}distance=length of tunnel+length of train

So,

For train A (length lll): tA=L+l30t_A = \frac{L+l}{30}tA​=30L+l​

For train B (length 4l4l4l): tB=L+4l20t_B = \frac{L+4l}{20}tB​=20L+4l​

Given that train A takes 35 35\,35s less time than train B: tB−tA=35t_B - t_A = 35tB​−tA​=35

Thus, L+4l20−L+l30=35\frac{L+4l}{20} - \frac{L+l}{30} = 3520L+4l​−30L+l​=35

  1. Use the given relation L=60lL=60lL=60l

Substitute L=60lL=60lL=60l: 60l+4l20−60l+l30=35\frac{60l+4l}{20} - \frac{60l+l}{30} = 352060l+4l​−3060l+l​=35

64l20−61l30=35\frac{64l}{20} - \frac{61l}{30} = 352064l​−3061l​=35

Take LCM 606060: 192l−122l60=35\frac{192l - 122l}{60} = 3560192l−122l​=35

70l60=35\frac{70l}{60} = 356070l​=35

7l6=35\frac{7l}{6} = 3567l​=35

l=35×67=30 ml = 35\times \frac{6}{7} = 30\ \text{m}l=35×76​=30 m

  1. Find tunnel length

L=60l=60×30=1800 mL = 60l = 60\times 30 = 1800\ \text{m}L=60l=60×30=1800 m

  1. Check options

L=1800 mL=1800\ \text{m}L=1800 m

So the correct option is C.

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