A disc of radius \(R\) rolls without slipping at speed \(v\) along positive \(x\)-axis. Velocity of point…
- \(\vec{v}_{p}=\left(v+\frac{v r \sin \theta}{R}\right) \hat{i}+\frac{v r \cos \theta}{R} \hat{j}\)
- \(\vec{v}_{\bar{F}}=\left(v+\frac{v r \sin \theta}{R}\right) \hat{i}-\frac{v r \cos \theta}{R} \hat{j}\)
- \(\vec{v}_{F}=\frac{v r \sin \theta}{R} \hat{i}+\frac{v r \cos \theta}{R} \hat{j}\)
- \(\vec{v}_{f}=\frac{\nu r \sin \theta}{R} \hat{i}-\frac{v r \cos \theta}{R} \hat{j}\)
Solution
\(\begin{array}{l}
\mathrm{V}_{\mathrm{P}_{\mathrm{x}}}=\left(\mathrm{v}+\frac{\mathrm{v}}{\mathrm{R}} \mathrm{r} \sin \theta\right) \hat{\mathrm{i}} \\
\mathrm{V}_{\mathrm{P}_{\mathrm{y}}}=-\left(\frac{\mathrm{v}}{\mathrm{R}} \mathrm{rcos} \theta\right) \hat{\mathrm{j}} \\
\therefore \overrightarrow{\mathrm{V}}_{\mathrm{P}}=\left(\mathrm{v}+\frac{\mathrm{vrsin} \theta}{\mathrm{R}}\right) \hat{\mathrm{i}}-\frac{\mathrm{vrcos} \theta}{\mathrm{R}} \hat{\mathrm{j}}
\end{array}\)
^Asked in: JEE Mains - Rotational Motion - Chapter Test