Category: HC Verma Part 1: Mechanics

Problem Statement Solve the Newton’s Laws / mechanics problem: Solve the Newton’s Laws / mechanics problem: A spring of spring constant $k = 200$ N/m is stretched by 5 cm. Find the restoring force. Hooke’s law: $F = kx$ Step 1: $x = 5$ cm $= 0.05$ m. Step 2: $F = kx = 200…

Problem Statement Solve the kinematics problem: Find the minimum speed at the top of a vertical circle of radius $r$ for a ball on a string to maintain circular motion. ($g = 10$ m/s², $r = 0.5$ m) All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts…

Problem Statement Solve the Newton’s Laws / mechanics problem: Solve the Newton’s Laws / mechanics problem: A 0.5 kg ball is whirled in a vertical circle of radius 1 m at constant speed 4 m/s. Find the tension at the bottom and top of the circle. ($g = 10$ m/s²) At bottom: $T – mg…

Problem Statement A person weighs 600 N on Earth. What is their weight on the Moon? (Moon’s gravity = $g_M = g/6$) 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…

Problem Statement Solve the Newton’s Laws / mechanics problem: Solve the Newton’s Laws / mechanics problem: Two point charges of $2\,\mu$C and $3\,\mu$C are 0.1 m apart. Find the force between them. ($k = 9\times10^9$ N m² C⁻²) $F = kq_1q_2/r^2$ Step 1: $F = \dfrac{9\times10^9\times2\times10^{-6}\times3\times10^{-6}}{(0.1)^2} = \dfrac{9\times10^9\times6\times10 Given Information See problem statement for all…

Problem Statement Analyze the circuit: Analyze the circuit: State Lami’s theorem. Three concurrent forces in equilibrium have magnitudes $F_1 = 10$ N, $F_2 = 12$ N. The angle between $F_1$ and $F_2$ is 120°. Find $F_3$. Lami’s theorem: $F_1/\sin\alpha_1 = F_2/\sin\alpha_2 = F_3/\sin\alpha_3$ where $\alpha_i$ is the angle opposite to $F_i Given Information See problem…

Problem Statement Analyze the circuit: Analyze the circuit: Three forces act on a particle in equilibrium: $F_1 = 10$ N (north), $F_2 = 10$ N (south), and $F_3 = ?$. Find $F_3$. Equilibrium: vector sum = 0 Step 1: $F_1 + F_2 = 10\hat{j} – 10\hat{j} = 0$. Step 2: For equilibrium, $F_3 = 0$…

Problem Statement Solve the Newton’s Laws / mechanics problem: Solve the Newton’s Laws / mechanics problem: Masses $m_1 = 1$ kg, $m_2 = 2$ kg, $m_3 = 3$ kg are placed in contact on a frictionless horizontal surface and pushed by a force $F = 18$ N. Find the acceleration and the force between $m_1$…

Problem Statement A rocket ejects mass at rate $\mu = 50\,\text{kg/s}$ with exhaust speed $u = 3000\,\text{m/s}$ relative to the rocket. Find the thrust force. Given Information $\mu = 50\,\text{kg/s}$ $u = 3000\,\text{m/s}$ Physical Concepts & Formulas The Tsiolkovsky rocket equation describes the motion of a rocket as it expels propellant. As the rocket ejects…

Problem Statement Why does a person feel weightless in a freely falling elevator? Explain in terms of forces. 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…