Ratio of Distance to Displacement in Circular Motion | JEE Physics | Doubtify JEE

🔄 Circular Motion | Physics | Doubtify JEE

🧮 Question:

A particle moves from point A to B in a circular path of radius $R$, covering an angle $\theta$(in radians), as shown in the figure. Find the ratio of the distance to the magnitude of displacement of the particle.

---

🖼️ Question Image:

🔍 Concept:

In circular motion, distance and displacement are not the same.

• Distance is the arc length the particle travels.

• Displacement is the chord length (shortest straight-line distance) between the initial and final positions.

---

🧠 Step-by-Step Solution:

Distance travelled = Arc length

$$\text{Distance} = R\theta$$

Displacement = Chord length between A and B

$$\text{Displacement} = 2R \sin\left(\frac{\theta}{2}\right)$$

Now, the ratio of distance to displacement is:

$$\text{Ratio} = \frac{\text{Distance}}{\text{Displacement}} = \frac{R\theta}{2R \sin(\theta/2)} = \frac{\theta}{2 \sin(\theta/2)}$$

✅ Final Answer:

$$\boxed{\frac{\theta}{2 \sin(\theta/2)}}$$

🖼️ Image Solution:

🎥 Video Solution:

🔍 Why this Question is Important:

This is a classic example from circular motion where students often confuse between path length (distance) and net displacement. Questions like these train you to think visually and conceptually. They often appear in early kinematics sections of JEE Mains and NEET.

---

📩 Have a Doubt?

Email us at doubtifyqueries@gmail.com or DM on Instagram @doubtifyjee

Stay consistent. Watch – Pause – Solve – Repeat.
Team Doubtify is with you till the finish line! 💪