Moments and centres of mass of discrete massesEdexcel A-Level Further Maths: Mind map

Exam questions on Moments and centres of mass of discrete masses

1. Three particles of masses 2 kg, 3 kg and 5 kg are placed on a straight line at the points $x=1$ m, $x=4$ m and $x=9$ m respectively, where $x$ is the distance from a fixed origin $O$ on the line. Take $g=9.8$ m s⁻².
   Find the total moment of the weights of the three particles about $O$.2 marks
2. Four particles of masses 1 kg, 2 kg, 3 kg and 4 kg are placed at the points with coordinates $(0,0)$, $(5,0)$, $(4,3)$ and $(1,3)$ respectively, where distances are in metres.
   Find the distance between the centre of mass and the 2 kg particle.2 marks
3. A uniform rod $AB$ has length 6 m and mass 12 kg. It rests horizontally on two smooth supports at $C$ and $D$, where $AC=1$ m and $DB=2$ m. Take $g=9.8$ m s⁻².
   Find the magnitudes of the reactions at $C$ and $D$.3 marks