Mathematics 9709 · AS & A Level · Probability

Probability — practice question

Particles $P$ and $Q$ have masses $0.8\,\text{kg}$ and $0.4\,\text{kg}$ respectively. $P$ is connected to a fixed point $A$ by a light inextensible string, and this string is inclined at an angle $\alpha$ to the vertical. $Q$ is connected to a fixed point $B$, vertically below $A$, by a light inextensible string of length $0.3\,\text{m}$. The string $BQ$ is horizontal. $P$ and $Q$ are linked to each other by a light inextensible string which is vertical. The particles move in horizontal circles of radius $0.3\,\text{m}$ about the axis through $A$ and $B$ with constant angular speed $5\,\text{rad s}^{-1}$ (see diagram).
(i)[3]

Using the motion of $Q$, determine the tensions in $PQ$ and $BQ$.

(ii)[5]

Find the tension in the string $AP$ together with the value of $\alpha$.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: Recognises the tension from weight as $T_{PQ} = 0.4g = 4\,\text{N}$

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