1. Given data

   • Radius of circular path: $r = 10\,\text{m}$
   • Time period: $T = 4\,\text{s}$
   • We need displacement after $t = 3\,\text{s}$ from the starting point.

2. Find angular displacement in 3 s In one complete revolution, the angle covered is $2\pi$ in $4\,$s.

   So angular speed is $\omega = \frac{2\pi}{T} = \frac{2\pi}{4} = \frac{\pi}{2}\,\text{rad/s}$

   Therefore, in $3\,$s, angular displacement is $\theta = \omega t = \frac{\pi}{2}\times 3 = \frac{3\pi}{2}$

   So the body has moved through $270^\circ$ from the starting point.

3. Displacement in circular motion Displacement is the straight-line distance between initial and final positions, i.e. the chord length.

   Chord length formula: $d = 2r\sin\frac{\theta}{2}$

   Substituting $r=10$ and $\theta=\frac{3\pi}{2}$: $d = 2(10)\sin\left(\frac{3\pi}{4}\right)$ $d = 20\cdot \frac{\sqrt{2}}{2}$ $d = 10\sqrt{2}\,\text{m}$

4. Check options

   • A: $15\pi$ ❌
   • B: $30$ ❌
   • C: $10\sqrt{2}$ ✅
   • D: $5\pi$ ❌

So the correct answer is Option C.