This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
C. 3m Step 1: Identify the forces and their positions. • Length of the beam HK, L = 10 m. • Weight of the uniform beam, W_b = 200 N. This acts at the center of the beam, which is L/2 = 10/2 = 5 m from H. • Weight of the man, W_m = 1000 N. This acts at point P, at a distance x from H (HP = x). • Reaction force at H, R_H = 800 N. • Reaction force at K, R_K = 400 N. Step 2: Apply the principle of moments. For the beam to be in rotational equilibrium, the sum of clockwise moments about any point must equal the sum of anticlockwise moments about the same point. Let's take moments about point H. Clockwise moments about H: • Moment due to the weight of the beam: W_b × (distance from H to center) • Moment due to the weight of the man: W_m × (distance from H to P) Anticlockwise moments about H: • Moment due to the reaction force at K: R_K × (distance from H to K) Step 3: Set up the moment equation. (W_b × 5 m) + (W_m × x) = (R_K × 10 m) Step 4: Substitute the given values into the equation. (200 N × 5 m) + (1000 N × x) = (400 N × 10 m) 1000 Nm + 1000x Nm = 4000 Nm Step 5: Solve for x. 1000x = 4000 - 1000 1000x = 3000 x = (3000)/(1000) x = 3 m The distance HP is 3 m. The final answer is C. 3m.