A uniform rod, AB, has length 4 metres - AQA - A-Level Maths Pure - Question 11 - 2018 - Paper 2

To find the value of x for equilibrium, we can use the principle of moments, which states that for an object to be in equilibrium, the clockwise moments must equal the counterclockwise moments around the pivot point, which in this case is point C.

1. Identify the moments:

   • The moment caused by the 4 kg mass which is located 0.6 m to the left of C:

   $ext{Moment}_{4 kg} = 4 ext{ kg} imes 0.6 ext{ m} = 2.4 ext{ kg m}$

   • The moment caused by the 1.5 kg mass which is located x m to the right of C:

   $ext{Moment}_{1.5 kg} = 1.5 ext{ kg} imes x ext{ m} = 1.5x ext{ kg m}$

2. Set up the equilibrium equation:

   $ext{Moment}_{4 kg} = ext{Moment}_{1.5 kg}$

   Therefore,

   $2.4 = 1.5x$

3. Solve for x:

   Rearranging gives us:

   x = rac{2.4}{1.5} = 1.6 ext{ m}

Thus, the value of x is 1.6 m.