Standard +0.3 This is a straightforward circular motion problem requiring application of Hooke's law and centripetal force equation. Students must equate tension (from elastic extension) to centripetal force and solve for extension—a standard two-step process with given values that substitute cleanly. While it's Further Maths content, the mechanics are routine once the setup is recognized.
One end of a light elastic string, of natural length \(a\) and modulus of elasticity \(3mg\), is attached to a fixed point \(O\) on a smooth horizontal plane. A particle \(P\) of mass \(m\) is attached to the other end of the string and moves in a horizontal circle with centre \(O\). The speed of \(P\) is \(\sqrt{\frac{1}{4}ga}\).
Find the extension of the string. [4]
One end of a light elastic string, of natural length $a$ and modulus of elasticity $3mg$, is attached to a fixed point $O$ on a smooth horizontal plane. A particle $P$ of mass $m$ is attached to the other end of the string and moves in a horizontal circle with centre $O$. The speed of $P$ is $\sqrt{\frac{1}{4}ga}$.
Find the extension of the string. [4]
\hfill \mbox{\textit{CAIE Further Paper 3 2021 Q1 [4]}}