Standard +0.3 This is a straightforward circular motion problem requiring students to apply Hooke's law and the centripetal force equation. The setup is standard with clearly given values, requiring substitution into F = mv²/r and T = λx/l, then solving a simple equation for l. It's slightly above average difficulty due to the algebraic manipulation needed, but follows a predictable method with no conceptual surprises.
A particle \(P\) of mass 0.3 kg moves in a circle with centre \(O\) on a smooth horizontal surface. \(P\) is attached to \(O\) by a light elastic string of modulus of elasticity 12 N and natural length \(l\) m. The speed of \(P\) is 4 m s\(^{-1}\), and the radius of the circle in which it moves is 2l m. Calculate \(l\). [4]
A particle $P$ of mass 0.3 kg moves in a circle with centre $O$ on a smooth horizontal surface. $P$ is attached to $O$ by a light elastic string of modulus of elasticity 12 N and natural length $l$ m. The speed of $P$ is 4 m s$^{-1}$, and the radius of the circle in which it moves is 2l m. Calculate $l$. [4]
\hfill \mbox{\textit{CAIE M2 2016 Q1 [4]}}