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
Another one ✨Fave — let's solve it. The question asks which pair of physical quantities has the same dimension. Step 1: Determine the dimensions of each quantity in the options. The fundamental dimensions are Mass (M), Length (L), and Time (T). Pressure: Force per unit area. Force (F) = mass × acceleration = M × LT^-2 = MLT^-2 Area (A) = L^2 Dimension of Pressure = FA = MLT^-2L^2 = ML^-1T^-2 Stress: Force per unit area. Dimension of Stress = FA = MLT^-2L^2 = ML^-1T^-2 Work: Force × distance. Dimension of Work = F × L = MLT^-2 × L = ML^2T^-2 Force: Mass × acceleration. Dimension of Force = MLT^-2 Velocity: Distance per unit time. Dimension of Velocity = LT = LT^-1 Acceleration: Change in velocity per unit time. Dimension of Acceleration = LT^-1T = LT^-2 Length: Fundamental dimension = L Mass: Fundamental dimension = M Step 2: Compare the dimensions for each pair in the options. A) Pressure and stress: Both have dimensions ML^-1T^-2. These are the same. B) Work and force: Work has ML^2T^-2, and Force has MLT^-2. These are different. C) Velocity and acceleration: Velocity has LT^-1, and Acceleration has LT^-2. These are different. D) Length and mass: Length has L, and Mass has M. These are different. Step 3: Conclude the correct option. The physical quantities with the same dimension are pressure and stress. The final answer is A Send me the next one 📸