Question 144: Centre of Mass and Rotational Motion

Question

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

Accepted Answer

$$
\begin{aligned}
& 	ext { Displacement of } C M=R \omega \frac{T}{2}=\pi r \\
& \Rightarrow 	ext { Displacement of } A =\sqrt{(2 R)^2+(\pi R)^2} \\
& =R \sqrt{\pi^2+4}
\end{aligned}
$$

Answer

$$R\sqrt {({\pi ^2} + 1)} $$

Answer

$$2R$$

Answer

$$R\sqrt {({\pi ^2} + 4)} $$

Answer

$$2R\sqrt {(1 + 4{\pi ^2})} $$

Centre of Mass and Rotational Motion

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

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