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Question

(A) The particle moves from point $A(r, 0)$ to point $B(0, r)$ along the circular arc.Path length is the distance covered along the circumference. Sin

Vedclass · Accepted Answer

$\frac{\pi r}{2}, r\sqrt{2}$

Vedclass · Answer

(A) The particle moves from point $A(r, 0)$ to point $B(0, r)$ along the circular arc.Path length is the distance covered along the circumference. Since the angle subtended at the center is $90^\circ$ (or $\frac{\pi}{2}$ radians),the path length is $s = r	heta = r 	imes \frac{\pi}{2} = \frac{\pi r}{2}$.Displacement is the straight-line distance between the initial point $A$ and final point $B$. Using the distance formula or vector subtraction:$\vec{r}_A = r\hat{i}$$\vec{r}_B = r\hat{j}$Displacement $\vec{d} = \vec{r}_B - \vec{r}_A = r\hat{j} - r\hat{i}$.The magnitude of displacement is $|\vec{d}| = \sqrt{(-r)^2 + (r)^2} = \sqrt{2r^2} = r\sqrt{2}$.Thus,the path length is $\frac{\pi r}{2}$ and the displacement is $r\sqrt{2}$.

$A$ particle moves along the circumference of a circle of radius $r$ from point $A$ to point $B$ as shown in the figure. What are the path length and displacement?

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