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
Step 1: Identify the pivot point and the forces acting on the metre rule. The metre rule is supported at the 40 cm mark, which is the pivot point. There are two forces creating moments: • The 15 g mass suspended at the 15 cm mark. • The mass of the metre rule, acting at its centre of mass at the 52.5 cm mark. Step 2: Calculate the perpendicular distances of the forces from the pivot. For the 15 g mass: Distance d_1 = 40 cm - 15 cm = 25 cm. This mass creates an anticlockwise moment. For the mass of the metre rule (M): Distance d_M = 52.5 cm - 40 cm = 12.5 cm. This mass creates a clockwise moment. Step 3: Apply the principle of moments. For the metre rule to be in equilibrium, the sum of the clockwise moments must equal the sum of the anticlockwise moments. Anticlockwise moment = Clockwise moment (15 g) × g × d_1 = M × g × d_M (15 g) × g × (25 cm) = M × g × (12.5 cm) Step 4: Solve for the mass of the metre rule (M). The acceleration due to gravity (g) cancels out from both sides. 15 g × 25 cm = M × 12.5 cm M = 15 g × 25 cm12.5 cm M = (375)/(12.5) g M = 30 g The mass of the metre rule is 30 g. Send me the next one 📸