3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{826ad8ff-6e5c-4224-88ba-e78b79d1bc21-04_542_469_219_735}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
A solid consists of a uniform solid right cylinder of height \(5 l\) and radius \(3 l\) joined to a uniform solid hemisphere of radius \(3 l\). The plane face of the hemisphere coincides with a circular end of the cylinder and has centre \(O\), as shown in Figure 2.
The density of the hemisphere is twice the density of the cylinder.
- Find the distance of the centre of mass of the solid from \(O\).
(5)
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{826ad8ff-6e5c-4224-88ba-e78b79d1bc21-04_618_807_1327_571}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
The solid is now placed with its circular face on a plane inclined at an angle \(\theta ^ { \circ }\) to the horizontal, as shown in Figure 3. The plane is sufficiently rough to prevent the solid slipping. The solid is on the point of toppling. - Find the value of \(\theta\).