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The displacement of a body when it covers a distance of \(C / 4\) (where, \(C\) is circumference) along the circumference of the circle of radius \(r\) with a uniform speed \(u\) is
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Verified Answer
The correct answer is:
\(r \sqrt{2}\)
The given situation is shown in the figure
When body covers \(\frac{C}{4}\) distance, where \(C\) is circumference, then it reaches from point \(A\) to \(B\) as shown in the figure.
\(\begin{aligned}
\therefore \text {Displacement, } A B & =\sqrt{O A^2+O B^2} \\
& =\sqrt{r^2+r^2}=\sqrt{2 r^2}=r \sqrt{2}
\end{aligned}\)
When body covers \(\frac{C}{4}\) distance, where \(C\) is circumference, then it reaches from point \(A\) to \(B\) as shown in the figure.
\(\begin{aligned}
\therefore \text {Displacement, } A B & =\sqrt{O A^2+O B^2} \\
& =\sqrt{r^2+r^2}=\sqrt{2 r^2}=r \sqrt{2}
\end{aligned}\)
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