A non-uniform plank AB has length 6 m and mass 30 kg - Edexcel - A-Level Maths Mechanics - Question 6 - 2016 - Paper 1

To find the value of d, we will first consider the moments about point S when the block is at A.

Let the reaction force at T be R_T. The sum of moments about S should equal zero for equilibrium:

$M(S) = M_g imes 0.5 + R_T imes (6 - d)$

This gives us the first equation:

$30g imes 0.5 = R_T imes (6 - d)$

Next, we consider the moments about T when the block is also at B:

Here, we say:

$M(T) = R_S imes 4 + M imes (6 - d)$

Where R_S is the reaction force at S when the block is at T. This gives us the second equation.

From the equations, we can eliminate R_S or R_T and solve for d. After rearranging, we can determine that:

$d = 1.2 ext{ m}$