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QJEEM23Ph5f0f: JEE Main 2023 Physics - Class 11 JEEM23Ph5f0f Solution: As shown in the figure, a particle is moving with constant…

As shown in the figure, a particle is moving with constant speed π m/s. Considering its motion from A to B, the magnitude of the average velocity is :

JEE Main 2023 (Online) 6th April Evening Shift Physics - Circular Motion Question 18 English

Multiple Choice Options

  • A π m/s
  • B 1.53 m/s
  • C 3 m/s
  • D 23 m/s

Step-by-Step Verified Solution

The given situation is shown below.

JEE Main 2023 (Online) 6th April Evening Shift Physics - Circular Motion Question 18 English Explanation
Given, v=πm/sv=\pi \mathrm{m} / \mathrm{s}

or

Rω=πω=πRrad/s[∵v=ωR]

Angular displacement, θ=120∘\theta=120^{\circ} or 2π3\frac{2 \pi}{3}

Using θ=ωt\theta=\omega t ,

t=θω=2π/3π/R=2R3

Linear displacement,

d=2Rsin⁡(θ/2)d=2Rsin⁡(120∘2)=2Rsin⁡60∘=2R32⇒R3

Average velocity =dt=R32R/3=332=1.53 m/s=\frac{d}{t}=\frac{R \sqrt{3}}{2 R / 3}=\frac{3 \sqrt{3}}{2}=1.5 \sqrt{3}\mathrm{~m} / \mathrm{s}

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