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Circular Motion question

2020 · 6 Sep · Shift 1 · Q47
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  5. /2020 · 6 Sep · Shift 1 · Q47

Circular Motion question

2020 · 6 Sep · Shift 1 · Q47

JEE MainPhysicsCircular MotionMCQ+4 / −1
A clock has a continuously moving second's hand of 0.1 m length. The average acceleration of the tip of the hand (in units of ms–2) is of the order of :
  1. A
    10-3
  2. B
    10-1
  3. C
    10-2
  4. D
    10-4
View written solutionFree

Correct answer: A

  1. Given data
  • Length of second hand: r=0.1 mr = 0.1\,\text{m}r=0.1m
  • The second hand completes one revolution in T=60 sT = 60\,\text{s}T=60s

So the angular speed is

ω=2πT=2π60=π30 rad s−1\omega = \frac{2\pi}{T} = \frac{2\pi}{60} = \frac{\pi}{30}\,\text{rad s}^{-1}ω=T2π​=602π​=30π​rad s−1
  1. Velocity of the tip

The speed of the tip is

v=ωr=π30×0.1=π300≈1.05×10−2 m s−1v = \omega r = \frac{\pi}{30}\times 0.1 = \frac{\pi}{300} \approx 1.05\times 10^{-2}\,\text{m s}^{-1}v=ωr=30π​×0.1=300π​≈1.05×10−2m s−1
  1. Average acceleration over 1 second

Since the hand moves continuously, in 1 s1\,\text{s}1s it turns through

Δθ=ωΔt=2π60×1=π30\Delta \theta = \omega \Delta t = \frac{2\pi}{60}\times 1 = \frac{\pi}{30}Δθ=ωΔt=602π​×1=30π​

The velocity changes direction by the same angle. For small angle Δθ\Delta\thetaΔθ, the change in velocity magnitude is

∣Δv⃗∣≈vΔθ|\Delta \vec v| \approx v\Delta\theta∣Δv∣≈vΔθ

Thus,

∣Δv⃗∣≈(π300)(π30)|\Delta \vec v| \approx \left(\frac{\pi}{300}\right)\left(\frac{\pi}{30}\right)∣Δv∣≈(300π​)(30π​) ∣Δv⃗∣≈1.1×10−3 m s−1|\Delta \vec v| \approx 1.1\times 10^{-3}\,\text{m s}^{-1}∣Δv∣≈1.1×10−3m s−1

Therefore average acceleration is

aavg=∣Δv⃗∣Δt≈1.1×10−31=1.1×10−3 m s−2a_{\text{avg}} = \frac{|\Delta \vec v|}{\Delta t} \approx \frac{1.1\times 10^{-3}}{1} = 1.1\times 10^{-3}\,\text{m s}^{-2}aavg​=Δt∣Δv∣​≈11.1×10−3​=1.1×10−3m s−2

So its order is

10−3 m s−210^{-3}\,\text{m s}^{-2}10−3m s−2
  1. Option check
  • A: 10−310^{-3}10−3 ✅
  • B: 10−110^{-1}10−1 ❌
  • C: 10−210^{-2}10−2 ❌
  • D: 10−410^{-4}10−4 ❌

Hence the correct option is A.

  1. Comparison with stored answer

Stored correct answer: A

This matches the derived answer.

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