Category: HC Verma Part 1: Mechanics

Problem Statement Solve the Newton’s Laws / mechanics problem: Solve the Newton’s Laws / mechanics problem: Earth orbits the Sun at radius $r = 1.5\times10^{11}$ m with period $T = 3.15\times10^7$ s. Find the centripetal acceleration. ($M_{\odot} = 2\times10^{30}$ kg, $G = 6.67\times10^{-11}$) $a_c = v^2/r = (2\pi r/T)^2/r = 4\pi^2 r/T^2$ Step 1: $a_c…

Problem Statement An apple of mass 0.2 kg falls toward Earth. By Newton’s third law, does Earth also accelerate toward the apple? Compare the accelerations. 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…

Problem Statement Solve the Newton’s Laws / mechanics problem: Solve the Newton’s Laws / mechanics problem: Two blocks of masses 2 kg and 3 kg are in contact on a frictionless surface. A force $F = 10$ N is applied on the 2 kg block. Find the acceleration and the contact force between the blocks.…

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 Solve the Newton’s Laws / mechanics problem: Solve the Newton’s Laws / mechanics problem: A horse pulls a cart. By Newton’s third law, the cart pulls back on the horse with equal force. Then how does the system move? Newton’s third law pairs act on different bodies; net force for each body includes…

Problem Statement Solve the Newton’s Laws / mechanics problem: A spring of natural length 10 cm and spring constant 500 N/m has a 2 kg mass hung from each end (vertically). By how much does the spring stretch? ($g = 10$ m/s²) All quantities, constants, and constraints stated in the problem above Physical constants used…

Problem Statement Solve the Newton’s Laws / mechanics problem: Solve the Newton’s Laws / mechanics problem: A block of mass 10 kg is suspended from two strings making angles 30° and 60° with the horizontal. Find the tensions $T_1$ (30°) and $T_2$ (60°). ($g = 10$ m/s²) Equilibrium: $T_1\cos30° + T_2\cos60° = $ horizontal balance;…

Problem Statement Solve the Newton’s Laws / mechanics problem: Solve the Newton’s Laws / mechanics problem: Name the four fundamental forces of nature and arrange them in decreasing order of strength. Strong nuclear, Electromagnetic, Weak nuclear, Gravitational Strong nuclear force: Strongest; range ~1 fm; holds nucleus together. Electromagnetic force: ~$10^{-2 Given Information See problem statement…

Problem Statement Solve the gravitation problem: Solve the Newton’s Laws / mechanics problem: Mass $m = 1$ kg is placed at the origin. Two masses $M = 10$ kg each are placed at $(0.5, 0)$ m and $(-0.5, 0)$ m. Find the net gravitational force on $m$. ($G = 6.67\times10^{-11}$ N m² kg⁻²) Gravitational force…

Problem Statement Solve the Newton’s Laws / mechanics problem: Solve the Newton’s Laws / mechanics problem: A block of mass 2 kg is on the floor of a car accelerating at 3 m/s². Find the pseudo force on the block as seen from the car’s frame. Pseudo force = $-m\vec{a}_{frame}$ (opposite to acceleration of non-inertial…