1 Fig. 1.1 shows a circular cylinder of mass 100 kg being raised by a light, inextensible vertical wire AB . There is negligible air resistance.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{bf477f61-9f8f-418a-86d8-392bc30323b1-1_306_256_368_965}
\captionsetup{labelformat=empty}
\caption{Fig. 1.1}
\end{center}
\end{figure}

(i) Calculate the acceleration of the cylinder when the tension in the wire is 1000 N .\\
(ii) Calculate the tension in the wire when the cylinder has an upward acceleration of $0.8 \mathrm {~m} \mathrm {~s} ^ { - 2 }$.

The cylinder is now raised inside a fixed smooth vertical tube that prevents horizontal motion but provides negligible resistance to the upward motion of the cylinder. When the wire is inclined at $30 ^ { \circ }$ to the vertical, as shown in Fig. 1.2, the cylinder again has an upward acceleration of $0.8 \mathrm {~m} \mathrm {~s} ^ { - 2 }$.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{bf477f61-9f8f-418a-86d8-392bc30323b1-1_308_490_1230_849}
\captionsetup{labelformat=empty}
\caption{Fig. 1.2}
\end{center}
\end{figure}

(iii) Calculate the new tension in the wire.

\hfill \mbox{\textit{OCR MEI M1  Q1 [8]}}