Category: HC Verma Part 1: Mechanics

Problem Statement Solve the Newton’s Laws / mechanics problem: Solve the Newton’s Laws / mechanics problem: A 0.1 kg ball tied to a string of length 0.5 m rotates in a horizontal circle at 2 rev/s. Find the tension in the string. ($g = 10$ m/s²) String is horizontal: $T = m\omega^2 r$ (assuming no…

Problem Statement Solve the Newton’s Laws / mechanics problem: Solve the Newton’s Laws / mechanics problem: A particle moves in a circle of radius 2 m. Its speed at a given instant is 4 m/s and is increasing at 3 m/s². Find the total acceleration at that instant. $a_c = v^2/r$; $a_t = dv/dt$; $a…

Problem Statement Solve the gravitation problem: Solve the gravitation problem: A satellite orbits Earth at height 300 km above the surface. Find its orbital speed and period. ($R_E = 6400$ km, $g = 9.8$ m/s²) $v = \sqrt{gR_E^2/r}$; $T = 2\pi r/v$; $r = R_E + h$ Step 1: $r = (6400+300)\times10^3 = 6.7\times10^6$ m.…

Problem Statement Solve the work-energy problem: Solve the work-energy problem: A ball of mass 0.2 kg at the bottom of a vertical circle (radius 1 m) has speed 8 m/s. Find the speed and tension at the side (horizontal position) and at the top. ($g = 10$ m/s²) Energy conservation; centripetal force equations At side…

Problem Statement A ball is attached to a rigid rod and swung in a vertical circle. Unlike a string, the rod can push as well as pull. What is the minimum speed at the top? Given Information See problem statement for all given quantities. Physical Concepts & Formulas Circular motion requires a centripetal force directed…

Problem Statement A ball hangs from a string of length 1.5 m. It is swung in a horizontal circle so that the string makes 53° with the vertical. Find the radius, speed, and period. ($g = 10$ m/s², $\sin53°=0.8$, $\cos53°=0.6$) Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem…

Problem Statement Solve the kinematics problem: Solve the kinematics problem: A wheel decelerates from 600 rpm to rest in 30 s. Find the angular deceleration and number of revolutions. $\omega_0 = 600 \times 2\pi/60 = 20\pi$ rad/s; $\alpha = \omega_0/t$; $N_{rev} = \theta/(2\pi)$ Step 1: $\omega_0 = 20\pi$ rad/s; $\alpha = 20\pi/30 = 2\pi/3$ rad/…

Problem Statement An electron (mass $9.1\times10^{-31}$ kg, charge $1.6\times10^{-19}$ C) moves at $10^7$ m/s perpendicular to a magnetic field of 0.1 T. Find the radius of the circular path. Given Information See problem statement for all given quantities. Physical Concepts & Formulas Circular motion requires a centripetal force directed toward the centre, providing the centripetal…

Problem Statement A person of mass 60 kg stands on the equator. How does their apparent weight differ from at the poles? ($g = 9.8$ m/s², $R_E = 6.4\times10^6$ m, $\omega = 7.27\times10^{-5}$ rad/s) Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the…

Problem Statement Solve the kinematics problem: Solve the kinematics problem: A particle moves in a circle at constant speed. In what direction does the acceleration point? What is the direction of the net force? Centripetal acceleration always points toward center; net force = centripetal force (toward center) Step 1: Since speed is constant, th Given…