Category: HC Verma Part 1: Mechanics

Problem Statement Solve the fluid mechanics problem: Find the dimensions and SI unit of pressure. Pressure = Force / Area $[P] = ML^{-1}T^{-2}$ Step 1: $P = F/A$. Step 2: $[F] = MLT^{-2}$, $[A] = L^2$. Step 3: $[P] = MLT^{-2}/L^2 = ML^{-1}T^{-2}$. $$\boxed{[P] = ML^{-1}T^{-2},\quad \text{SI unit} = \text{Pa (pascal)}}$$ Given Information See problem…

Problem Statement Solve the work-energy problem: Find the dimensions and SI unit of energy (work). Work = Force × displacement $[E] = ML^2T^{-2}$ Step 1: $W = F \cdot d$. Step 2: $[F] = MLT^{-2}$, $[d] = L$. Step 3: $[W] = MLT^{-2} \times L = ML^2T^{-2}$. $$\boxed{[E] = ML^2T^{-2},\quad \text{SI unit} = \text{J (joule)}}$$…

Problem Statement Solve the Newton’s Laws / mechanics problem: Find the dimensions and SI unit of force. Newton’s second law: $F = ma$ $[F] = MLT^{-2}$ Step 1: $F = ma$. Step 2: $[m] = M$, $[a] = LT^{-2}$. Step 3: $[F] = M \cdot LT^{-2} = MLT^{-2}$. $$\boxed{[F] = MLT^{-2},\quad \text{SI unit} = \text{N…

Problem Statement Solve the kinematics problem: Find the dimensions and SI unit of acceleration. Acceleration = rate of change of velocity $[a] = LT^{-2}$ Step 1: $a = \Delta v / \Delta t$. Step 2: $[\Delta v] = LT^{-1}$, $[\Delta t] = T$. Step 3: $[a] = LT^{-1}/T = LT^{-2}$. $$\boxed{[a] = LT^{-2},\quad \text{SI unit}…

Problem Statement Find the dimensions of speed. What is its SI unit? Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation laws and equations of motion, then solving systematically with careful attention to units…