Moderate -0.8 This is a straightforward statics problem requiring only basic equilibrium principles. Students must recognize that tension equals the weight of the hanging particle (3g), then resolve forces perpendicular to the plane using the given cosine value. It involves standard techniques with no problem-solving insight needed, making it easier than average but not trivial since it requires careful resolution of forces on an inclined plane.
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\includegraphics[max width=\textwidth, alt={}, center]{f23ea8e7-9b81-4192-8c20-8c46aabfecca-2_446_497_258_826}
A small ball \(B\) of mass 4 kg is attached to one end of a light inextensible string. A particle \(P\) of mass 3 kg is attached to the other end of the string. The string passes over a fixed smooth pulley. The system is in equilibrium with the string taut and its straight parts vertical. \(B\) is at rest on a rough plane inclined to the horizontal at an angle of \(\alpha\), where \(\cos \alpha = 0.8\) (see diagram). State the tension in the string and find the normal component of the contact force exerted on \(B\) by the plane.
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\includegraphics[max width=\textwidth, alt={}, center]{f23ea8e7-9b81-4192-8c20-8c46aabfecca-2_446_497_258_826}
A small ball $B$ of mass 4 kg is attached to one end of a light inextensible string. A particle $P$ of mass 3 kg is attached to the other end of the string. The string passes over a fixed smooth pulley. The system is in equilibrium with the string taut and its straight parts vertical. $B$ is at rest on a rough plane inclined to the horizontal at an angle of $\alpha$, where $\cos \alpha = 0.8$ (see diagram). State the tension in the string and find the normal component of the contact force exerted on $B$ by the plane.
\hfill \mbox{\textit{CAIE M1 2015 Q1 [3]}}