In figure, a sphere of radius \(2 \mathrm{~m}\) rolls on a plank. The accelerations of the sphere and the…

In figure, a sphere of radius \(2 \mathrm{~m}\) rolls on a plank. The accelerations of the sphere and the plank are indicated. Find the value of \(\alpha\) in \(\mathrm{rad} / \mathrm{s}^{2}\).

Solution

Acceleration of point A must be equal to the acceleration of the plank due to pure rolling.
\(\begin{array}{l}
a_{r}-a_{2}=a_{1} \\
a(2)-4=2 \Longrightarrow a=3 \mathrm{rad} / \mathrm{s}^{2}
\end{array}\)

Asked in: JEE Mains - Rotational Motion - Chapter Test

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