Standard +0.3 This is a straightforward circular motion problem requiring application of Hooke's law and centripetal force equation. With only 3 marks, it involves setting T = λx/l equal to mrω², then solving for x - a standard exercise with no conceptual difficulty beyond knowing the basic formulas.
A particle of mass \(2\) kg is attached to one end of a light elastic string of natural length \(0.8\) m and modulus of elasticity \(100\) N. The other end of the string is attached to a fixed point \(O\) on a smooth horizontal surface. The particle is moving in a horizontal circle about \(O\) with the string taut and with constant angular speed \(5\) radians per second.
Find the extension of the string. [3]
A particle of mass $2$ kg is attached to one end of a light elastic string of natural length $0.8$ m and modulus of elasticity $100$ N. The other end of the string is attached to a fixed point $O$ on a smooth horizontal surface. The particle is moving in a horizontal circle about $O$ with the string taut and with constant angular speed $5$ radians per second.
Find the extension of the string. [3]
\hfill \mbox{\textit{CAIE Further Paper 3 2024 Q1 [3]}}