Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
$OA$ is a rod that turns in a horizontal circle about a vertical axis passing through $O$. A particle $P$ with mass $0.2\,\text{kg}$ is fixed to the midpoint of a light inextensible string. One end of the string is fastened to the rod at $A$, and the other end is fastened to a point $B$ on the axis. It is given that $OA = OB$, angle $OAP =$ angle $OBP = 30^\circ$, and $P$ is $0.4\,\text{m}$ from the axis. The rod and the particle rotate together about the axis, with $P$ lying in the plane $OAB$ (see diagram).
(i)[6]
Calculate the tensions in the two sections of the string when the speed of $P$ is $1.2\,\text{m s}^{-1}$.
(ii)[6]
The angular speed of the rod is raised to $5\,\text{rad s}^{-1}$, and the system is now stated to rotate with angle $OAP =$ angle $OBP = 60^\circ$. Show that the tension in the $AP$ segment of the string is zero.
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Resolving vertically gives $B\cos30-A\sin30=0.2g$” …