Torque Angular Momentum And Equilibrium Problems - Physics 11th - Chapter 5 - Sindh Textbook Board (stb problems)

  

TORQUE ANGULAR MOMENTUM 

AND EQUILIBRIUM

 (PROBLEMS)

Problem 5.1. Locate the centre of mass of a system of particles each of mass 'm', arranged to correspond in position to the six corners of a regular (planar) hexagon.

Problem 5.2. Find the position of centre of mass of five equal-mass particles located at the five corners of a square-based right pyramid with sides of length 'l' and altitude 'h'. 

Problem 5.3. The mass of the sun is 329390 times the earth's mass and the mean distance from the centre of the sun to the centre of the earth is 1.496 × 10^8km. Treating the earth and sun as particles with each mass concentrated at the respective geometric centre, how far from the centre of the sun is the C.M (centre of mass) of the earth-sun system? Compare this distance with the mean radius of the sun (6.9960 × 10^5km)

Problem 5.4. A particle of mass 4 kg moves along the x-axis with a velocity v = 15t m/s, where t = 0 is the instant that the particle is at the origin. (a) at t=2s, what is the angular momentum of the particle about a point P located on the +y-axis, 6m from the origin. (b) what torque about P acts on the particle?

Problem 5.5. A particle of mass 'm' is located at the vector position r and has a linear momentum vector P. The vector r and P are non zero. If the particle moves only in the x, y plane, prove that Lx = Ly = 0 and Lz ≠ 0.

Problem 5.6. A light rigid rod Im in length rotates in the xy-plane about a pivot through the rod's centre. Two particles of mass 2kg and 3kg are connected to its ends. Determined the angular momentum of the system about the origin at the instant the speed of each particle is 5m/s.

Problem 5.7. A uniform beam of mass 'M' supports two masses m1 and m2. If the knife edge of the support is under the beam's centre of gravity and my is at a distance 'd' from the centre, determine the position of m2 such that the system is balanced.

Problem 5.8. A uniform ladder of length I and weight W = 50 N rests against a smooth vertical wall. If the coefficient of friction between the ladder and the ground is 0.40, find the minimum angle θmin such that the ladder may not slip.

Problem 5.9. A ladder with a uniform density and a mass 'm' rests against a frictionless vertical wall at an angle of 60°. The lower end rests on a flat surface where the coefficient of friction (static) is 0.40. A student with a mass (M = 2m) attempts to climb the ladder. What fraction of the length 'L' of the ladder will the student have reached when the ladder begins to slip?

Problem 5.10. A particle of mass 0.3 kg moves in the xy-plane. At the instant its coordinates are (2, 4)m, its velocity is (3i+4j)m/s. At this instant determine the angular momentum of the particle relative to the origin.

Problem 5.11. A uniform horizontal beam of length 8m and weighing 200N is pivoted at the wall with its far end supported by a cable that makes an angle of 53° with the horizontal. If a person weighing 600N stands 2m from the wall, find the tension and the reaction force at the pivot.