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
Welcome back — missed you this week. Here are the solutions to the questions: Question 9: Step 1: Identify the forces, their positions, and the pivot point. The meter rule is uniform, so its weight W acts at the 50 cm mark. The pivot R is at the 70 cm mark. Force at Q is F_Q = 0.1 \, N at the 60 cm mark. Force at S is F_S = 0.4 \, N at the 85 cm mark. Step 2: Calculate the distances of each force from the pivot R. Distance of F_Q from R: d_Q = 70 \, cm - 60 \, cm = 10 \, cm = 0.1 \, m. This creates an anticlockwise moment. Distance of W from R: d_W = 70 \, cm - 50 \, cm = 20 \, cm = 0.2 \, m. This creates an anticlockwise moment. Distance of F_S from R: d_S = 85 \, cm - 70 \, cm = 15 \, cm = 0.15 \, m. This creates a clockwise moment. Step 3: Apply the principle of moments for equilibrium (sum of anticlockwise moments = sum of clockwise moments). (F_Q × d_Q) + (W × d_W) = (F_S × d_S) (0.1 \, N × 0.1 \, m) + (W × 0.2 \, m) = (0.4 \, N × 0.15 \, m) 0.01 \, Nm + 0.2W = 0.06 \, Nm Step 4: Solve for W. 0.2W = 0.06 - 0.01 0.2W = 0.05 W = (0.05)/(0.2) W = 0.25 \, N The weight of the meter rule is A. 0.25N. Question 10: Step 1: Define the positions of the masses. Assume the meter rule extends from 0 cm to 100 cm. Lighter mass m_1 = 40 \, g is at x_1 = 0 \, cm. Heavier mass m_2 = 60 \, g is at x_2 = 100 \, cm. Step 2: Calculate the center of gravity (X_CG) using the formula X_CG = ( m_i x_i)/( m_i). X_CG = ((m_1 × x_1) + (m_2 × x_2))/(m_1 + m_2) X_CG = (40 \, g × 0 \, cm) + (60 \, g × 100 \, cm)40 \, g + 60 \, g X_CG = 0 + 6000 \, g cm100 \, g X_CG = 60 \, cm Step 3: Interpret the result in relation to the options. The center of gravity is at the 60 cm mark. Option C states "40cm from the heavier mass". The heavier mass is at 100 cm. 100 \, cm - 40 \, cm = 60 \, cm. This matches our calculated position. The center of gravity of the system is C. 40cm from the heavier mass. Question 11: Step 1: Identify the forces, their positions, and the pivot point. The meter rule QR is uniform, so its mass M acts at the 50 cm mark (midpoint of QR, assuming Q is 0 cm and R is 100 cm). A mass of m_P = 10 \, g is hung at P, 10 cm from Q. So P is at the 10 cm mark. The knife edge (pivot) is 55 cm from R. This means the pivot is at 100 \, cm - 55 \, cm = 45 \, cm from Q. Step 2: Calculate the distances of each mass from the pivot (45 cm mark). Distance of m_P from pivot: d_P = 45 \, cm - 10 \, cm = 35 \, cm. This creates an anticlockwise moment. Distance of rule's mass M from pivot: d_M = 50 \, cm - 45 \, cm = 5 \, cm. This creates a clockwise moment. Step 3: Apply the principle of moments for equilibrium. (m_P × d_P) = (M × d_M) (10 \, g × 35 \, cm) = (M × 5 \, cm) 350 \, g cm = M × 5 \, cm Step 4: Solve for M. M = 350 \, g cm5 \, cm M = 70 \, g The mass of the meter rule is C. 70g. Question 12: Step 1: Identify the force and the pivot point. The force F = 5 \, N acts at point Y. The pivot point is X. Step 2: Identify the perpendicular distance from the pivot to the line of action of the force. The distance between X and Y is XY = 2 \, m. The diagram shows the force acting perpendicular to the rod at Y. Step 3: Calculate the moment of the force about point X using the formula Moment = Force × Perpendicular distance. Moment = F × XY Moment = 5 \, N × 2 \, m Moment = 10 \, Nm The moment of the force about point X is D. 10 Nm. Send me the next one 📸