Standard +0.3 This is a standard conical pendulum problem requiring resolution of forces (tension into horizontal and vertical components), application of circular motion (centripetal force = mv²/r), and elimination of tension. The setup is straightforward with cos θ given explicitly, making it slightly easier than average. It's a routine 4-mark question testing basic circular motion principles without requiring novel insight.
One end of a light inextensible string of length \(a\) is attached to a fixed point \(O\). The other end of the string is attached to a particle of mass \(m\). The string is taut and makes an angle \(\theta\) with the downward vertical through \(O\), where \(\cos \theta = \frac{2}{3}\). The particle moves in a horizontal circle with speed \(v\).
Find \(v\) in terms of \(a\) and \(g\). [4]
One end of a light inextensible string of length $a$ is attached to a fixed point $O$. The other end of the string is attached to a particle of mass $m$. The string is taut and makes an angle $\theta$ with the downward vertical through $O$, where $\cos \theta = \frac{2}{3}$. The particle moves in a horizontal circle with speed $v$.
Find $v$ in terms of $a$ and $g$. [4]
\hfill \mbox{\textit{CAIE Further Paper 3 2023 Q1 [4]}}