Mathematics 9709 · AS & A Level · Probability

Probability — practice question

A particle $P$ with mass $0.1\,\text{kg}$ is fastened to one end of a light inextensible string of length $0.5\,\text{m}$. The other end of the string is fixed at point $A$. Particle $P$ travels round a circle whose centre $O$ lies on a smooth horizontal surface $0.3\,\text{m}$ below $A$. The string tension has magnitude $T\,\text{N}$ and the magnitude of the force exerted on $P$ by the surface is $R\,\text{N}$.
(i)[4]

If the speed of $P$ is $1.5\,\text{m s}^{-1}$, calculate $T$ and $R$.

(ii)[4]

If instead $T = R$, calculate the angular speed of $P$.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: Apply Newton's Second Law in the horizontal direction: $0.1\times 1.5^2/0.4 = T\cos\theta$

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