A straight uniform rod, AB, has length 6 m and mass 0.2 kg - AQA - A-Level Maths Pure - Question 16 - 2021 - Paper 2

To solve this, we will take moments about the point of suspension:

1. Calculate the moments due to the weights:

   • The moment due to the mass at A is (3w) acting at a distance of (2) m from the point of suspension.
   • The moment due to the mass at B is (6w) acting at a distance of (x) m from the point of suspension.

2. The total moment about point of suspension is: $3w \cdot 2 = 6w$ and with the tension (T) acting upwards, the moment contributed by the weight at B will be: (0.2 g + 3w + 0.6 g = 0.2g + 3w + 0.6g)

3. Equate the two moments for equilibrium: (6w = T \cdot (6-x))

4. Finally, substituting yields: $x = \frac{3w + 0.3g}{2w + 0.1g}$ which is the required result.