The displacement of a body when it covers a distance of \(C / 4\) (where, \(C\) is circumference) along the…

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
  1. \(r\)
  2. \(r \sqrt{2}\)
  3. \(2 r\)
  4. \(\frac{r}{2}\)

Solution

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. \(\begin{aligned} \therefore \text {Displacement, } A B & =\sqrt{O A^2+O B^2} \\ & =\sqrt{r^2+r^2}=\sqrt{2 r^2}=r \sqrt{2} \end{aligned}\)

Asked in: AP EAMCET 2020 (18 Sep Shift 1)

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