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Circular Motion question

2023 · 13 Apr · Shift 2 · Q49
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  5. /2023 · 13 Apr · Shift 2 · Q49

Circular Motion question

2023 · 13 Apr · Shift 2 · Q49

JEE MainPhysicsCircular MotionMCQ+4 / −1
A vehicle of mass 200 kg200 \mathrm{~kg}200 kg is moving along a levelled curved road of radius 70 m70 \mathrm{~m}70 m with angular velocity of 0.2 rad/s0.2 ~\mathrm{rad} / \mathrm{s}0.2 rad/s. The centripetal force acting on the vehicle is:
  1. A
    560 N560 \mathrm{~N}560 N
  2. B
    14 N14 \mathrm{~N}14 N
  3. C
    2800 N2800 \mathrm{~N}2800 N
  4. D
    2240 N2240 \mathrm{~N}2240 N
View written solutionFree

Correct answer: A

  1. Given data
  • Mass of vehicle: m=200 kgm = 200\,\text{kg}m=200kg
  • Radius of curved road: r=70 mr = 70\,\text{m}r=70m
  • Angular velocity: ω=0.2 rad/s\omega = 0.2\,\text{rad/s}ω=0.2rad/s
  1. Formula for centripetal force

For motion in a circle,

Fc=mω2rF_c = m\omega^2 rFc​=mω2r

  1. Substitute the values

Fc=200×(0.2)2×70F_c = 200 \times (0.2)^2 \times 70Fc​=200×(0.2)2×70

First compute:

(0.2)2=0.04(0.2)^2 = 0.04(0.2)2=0.04

So,

Fc=200×0.04×70F_c = 200 \times 0.04 \times 70Fc​=200×0.04×70

Fc=8×70F_c = 8 \times 70Fc​=8×70

Fc=560 NF_c = 560\,\text{N}Fc​=560N

  1. Match with the options
  • A: 560 N560\,\text{N}560N ✅
  • B: 14 N14\,\text{N}14N
  • C: 2800 N2800\,\text{N}2800N
  • D: 2240 N2240\,\text{N}2240N

Therefore, the correct answer is Option A.

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