Category: HC Verma Part 1: Mechanics

Problem Statement If $|\vec{A}| = 4$, $|\vec{B}| = 3$, and the angle between them is 60°, find $|\vec{A}\times\vec{B}|$. 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…

Problem Statement Find the component of vector $\vec{A}$ of magnitude 5 m along a direction making 30° with it, and perpendicular to that direction. 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…

Problem Statement If $|\vec{A}| = 4$ and $|\vec{B}| = 3$ with angle 60° between them, find $\vec{A}\cdot\vec{B}$. 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…

Problem Statement Vectors $\vec{A}$ (magnitude 3) and $\vec{B}$ (magnitude 4) are inclined at 60°. Find the angle $\alpha$ made by the resultant with $\vec{B}$. 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…

Problem Statement Two vectors $\vec{A}$ and $\vec{B}$ have magnitudes 3 and 4 respectively and the angle between them is 60°. Find the magnitude of their resultant. 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…

Problem Statement Using dimensional analysis, derive the formula for the time period $T$ of a simple pendulum depending on length $l$ and $g$. 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…

Problem Statement Check the dimensional consistency of $s = ut + \frac{1}{2}at^2$. 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…

Problem Statement Check the dimensional consistency of $v = u + at$. 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…

Problem Statement Solve the work-energy problem: Find the dimensions and SI unit of power. Power = Work / Time Step 1: $P = W/t$, $[W] = ML^2T^{-2}$, $[t] = T$. Step 2: $[P] = ML^2T^{-3}$. $$\boxed{[P] = ML^2T^{-3},\quad \text{SI unit} = \text{W (watt)}}$$ Given Information See problem statement for all given quantities. Physical Concepts &…

Problem Statement Solve the fluid mechanics problem: Find the dimensions of coefficient of viscosity $\eta$. Newton’s viscosity law: $F = \eta A (dv/dy)$ Step 1: $\eta = F / (A \cdot dv/dy)$. Step 2: $[dv/dy] = (LT^{-1})/L = T^{-1}$. Step 3: $[\eta] = MLT^{-2}/(L^2 \cdot T^{-1}) = ML^{-1}T^{-1}$. $$\boxed{[\eta] = ML^{-1}T^{-1},\quad \text{SI unit} = Given…