a) The two conditions for a rigid body to be in equilibrium under a number of coplanar forces are:

Here is the solution to the problem: a) The two conditions for a rigid body to be in equilibrium under a number of coplanar forces are: • The vector sum of all external forces acting on the body must be zero. This ensures translational equilibrium. • The vector sum of all external torques (or moments) about any point must be zero. This ensures rotational equilibrium. b) To determine the reactions at A and B, we apply the conditions for equilibrium. Step 1: Identify all forces and their positions. • Weight of the uniform beam: W = 100\, N acting at the center of the beam, which is at 5\, m2 = 2.5\, m from A. • Downward force: F_1 = 200\, N at 1\, m from A. • Downward force: F_2 = 100\, N at 4\, m from A. • Upward reaction force at A: R_A. • Upward reaction force at B: R_B. The total length of the beam is 5\, m. Step 2: Apply the condition for translational equilibrium (sum of vertical forces is zero). R_A + R_B - F_1 - W - F_2 = 0 R_A + R_B - 200\, N - 100\, N - 100\, N = 0 R_A + R_B = 400\, N (1) Step 3: Apply the condition for rotational equilibrium (sum of moments about any point is zero). Let's take moments about point A to find R_B. Clockwise moments = Anti-clockwise moments (F_1 × 1\, m) + (W × 2.5\, m) + (F_2 × 4\, m) = (R_B × 5\, m) (200\, N × 1\, m) + (100\, N × 2.5\, m) + (100\, N × 4\, m) = (R_B × 5\, m) 200\, Nm + 250\, Nm + 400\, Nm = 5 R_B\, m 850\, Nm = 5 R_B\, m Step 4: Calculate R_B. R_B = 850\, Nm5\, m R_B = 170\, N Step 5: Substitute R_B into Equation (1) to find R_A. R_A + 170\, N = 400\, N R_A = 400\, N - 170\, N R_A = 230\, N The reactions at A and B are: R_A = 230 N R_B = 170 N Drop the next question 📸