Question 231: Work, Energy and Power & Circular Motion

Question

A wheel of radius 1 m rolls through $180^{\circ}$ over a plane surface. The magnitude of the displacement of the point of the wheel initially in contact with the surface is.

Accepted Answer

Distance travelled by the wheel in half revolution $=\frac{\mathrm{C}}{2}=\frac{2 \pi \mathrm{r}}{2}=\pi \mathrm{r}$
Where C is the circumference of the wheel.
$	herefore \quad$ From figure,
Displacement of initial point of contact after half revolution $=\mathrm{AB}$
$$\begin{aligned}
& 	herefore \quad \mathrm{AB}^2=\mathrm{AD}^2+\mathrm{DB}^2 \
& \mathrm{AB}^2=(\pi r)^2+(2 \mathrm{r})^2=\mathrm{r}^2\left(\pi^2+4ight) \
& 	herefore \quad \mathrm{AB}=\mathrm{r} \sqrt{\left(\pi^2+4ight)} \
& 	herefore \quad \mathrm{AB}=\sqrt{\left(\pi^2+4ight)}\quad	ext{.... (given)}
\end{aligned}$$

Answer

$2 \pi$

Answer

$\pi$

Answer

$\sqrt{\pi^2+4}$

Answer

$3 \pi$

Work, Energy and Power & Circular Motion

A wheel of radius 1 m rolls through 180^{\circ} over a plane surface. The magnitude of the displacement of the point of the wheel initially in contact with the surface is.

Choose the correct answer: