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JIPMER 2019
Exam
JIPMER
Year
2019
Subject
Physics
Chapter
Work, Power and Energy

JIPMER 2019 · Physics · Work, Power and Energy

A particle is moving with 10 ~m / s in a circle of radius 5 m ,...

A particle is moving with 10 m/s10 \mathrm{~m} / \mathrm{s} in a circle of radius 5 m , find out magnitude of average velocity if particle moved by 60∘60^{\circ} in 1 sec.

Options

  1. A5 m/s5 \mathrm{~m} / \mathrm{s}
  2. B10 m/s10 \mathrm{~m} / \mathrm{s}
  3. C53 m/s5 \sqrt{3} \mathrm{~m} / \mathrm{s}
  4. D20 m/s20 \mathrm{~m} / \mathrm{s}

Correct answer

A. 5 m/s5 \mathrm{~m} / \mathrm{s}

Step-by-step solution

 Given, velocity of particle v=10m/s radius (r′)=5m Angular displacement (θ)=60∘∴θ=60×π180rad⇒θ=π3rad\begin{aligned} & \text{ Given, velocity of particle } v=10 \mathrm{ m} / \mathrm{s} \\ & \text{ radius }\left(r^{\prime}\right)=5 \mathrm{ m} \\ & \text{ Angular displacement }(\theta)=60^{\circ} \\ & \therefore \quad \theta=60 \times \frac{\pi}{180} \mathrm{rad} \\ & \Rightarrow \quad \theta=\frac{\pi}{3} \mathrm{rad} \\ & \end{aligned} When particle moves at an angle of 60∘60^{\circ}, then according to figure, displacement AB is equal to radius rr because it forms an equilateral triangle. ∴\therefore Average velocity = displacement AB time =r′1=5m/=\frac{\text{ displacement } \mathrm{AB}}{\text{ time }}=\frac{\mathrm{r}^{\prime}}{1}=5 \mathrm{ m} /s\mathrm{s}
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