CAIE M2 2015 June — Question 5

Exam BoardCAIE
ModuleM2 (Mechanics 2)
Year2015
SessionJune
TopicMoments

5
\includegraphics[max width=\textwidth, alt={}, center]{a03ad6c1-b4a3-4007-8d3b-ce289a998a55-3_499_721_715_712} A uniform solid cube with edges of length 0.4 m rests in equilibrium on a rough plane inclined at an angle of \(30 ^ { \circ }\) to the horizontal. \(A B C D\) is a cross-section through the centre of mass of the cube, with \(A B\) along a line of greatest slope. \(B\) lies below the level of \(A\). One end of a light elastic string with modulus of elasticity 12 N and natural length 0.4 m is attached to \(C\). The other end of the string is attached to a point below the level of \(B\) on the same line of greatest slope, such that the string makes an angle of \(30 ^ { \circ }\) with the plane (see diagram). The cube is on the point of toppling. Find
  1. the tension in the string,
  2. the weight of the cube.