Standard +0.3 This is a standard M2 circular motion problem with two strings at specified angles. Part (ii) requires resolving forces in vertical and horizontal directions, applying F=mrω², and solving simultaneous equations - all routine techniques for this module. The geometry is given explicitly (angles 30° and 60°, radius 1.5m), making it slightly easier than average M2 questions that require students to find geometric relationships themselves.
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The lower part of the string is now attached to a point \(R\), vertically below \(P\). \(P B\) makes an angle \(30 ^ { \circ }\) with the vertical and \(R B\) makes an angle \(60 ^ { \circ }\) with the vertical. The bead \(B\) now moves in a horizontal circle of radius 1.5 m with constant speed \(v _ { \mathrm { m } } \mathrm { m } ^ { - 1 }\) (see Fig. 2).
\begin{enumerate}[label=(\alph*)]
\item Show that the tension in the string is 4.16 N , correct to 3 significant figures.
\item Calculate $\omega$.\\
(ii)
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\caption{Fig. 2}
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The lower part of the string is now attached to a point $R$, vertically below $P$. $P B$ makes an angle $30 ^ { \circ }$ with the vertical and $R B$ makes an angle $60 ^ { \circ }$ with the vertical. The bead $B$ now moves in a horizontal circle of radius 1.5 m with constant speed $v _ { \mathrm { m } } \mathrm { m } ^ { - 1 }$ (see Fig. 2).\\
(a) Calculate the tension in the string.\\
(b) Calculate $v$.
\end{enumerate}
\hfill \mbox{\textit{OCR M2 2008 Q6 [11]}}