A disc is rolling without slipping on a surface. The radius of the disc is $R$. At $t=0$, the top most point…

A disc is rolling without slipping on a surface. The radius of the disc is $R$. At $t=0$, the top most point on the disc is $\mathrm{A}$ as shown in figure. When the disc completes half of its rotation, the displacement of point $A$ from its initial position is

1. $\mathrm{R} \sqrt{\left(\pi^2+4\right)}$
2. $\mathrm{R} \sqrt{\left(\pi^2+1\right)}$
3. $2 \mathrm{R}$
4. $2 \mathrm{R} \sqrt{\left(1+4 \pi^2\right)}$

Solution

(a) From figure,


Displacement,
$\mathrm{BA}=\sqrt{(2 \mathrm{R})^2+(\pi \mathrm{R})^2}=\mathrm{R} \sqrt{4+\pi^2}$

Asked in: BITSAT 2023 (Memory Based Paper 1)

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