Moderate -0.5 This is a straightforward application of circular motion formulas requiring only two steps: equate tension to centripetal force (4mg = mv²/a) to find speed, then use T = 2πa/v. Standard bookwork with no conceptual challenges, though the Further Mechanics context places it slightly above typical AS-level questions.
A particle \(P\) of mass \(m\) is attached to one end of a light inextensible string of length \(a\). The other end of the string is attached to a fixed point \(O\) on a smooth horizontal plane. The particle \(P\) moves in horizontal circles about \(O\). The tension in the string is \(4mg\).
Find, in terms of \(a\) and \(g\), the time that \(P\) takes to make one complete revolution. [2]
A particle $P$ of mass $m$ is attached to one end of a light inextensible string of length $a$. The other end of the string is attached to a fixed point $O$ on a smooth horizontal plane. The particle $P$ moves in horizontal circles about $O$. The tension in the string is $4mg$.
Find, in terms of $a$ and $g$, the time that $P$ takes to make one complete revolution. [2]
\hfill \mbox{\textit{CAIE Further Paper 3 2020 Q1 [2]}}