A mass M is hung with a light inextensible string. Tension...

A mass $M$ is hung with a light inextensible string. Tension in horizontal part of string is
(Figure can't copy)
(a) $\sqrt{3} \mathrm{Mg}$
(b) $\sqrt{2} M g$
(c) $\frac{M g}{\sqrt{3}}$
(d) $\frac{M g}{2}$

Key Concepts

Tension in Light, Inextensible Strings

In many mechanics problems, a light and inextensible string is assumed to have negligible mass and not to stretch. This means that, in the absence of friction, the tension is transmitted uniformly along the string, making it easier to analyze the forces acting on various parts of the system.

Static Equilibrium

When a system is at rest, all the forces acting on it must balance such that the net force in every direction is zero. In problems involving a hanging mass, the tension in different segments of the string must interact with gravitational forces (and possibly other forces) in a way that satisfies equilibrium conditions.

Vector Resolution of Forces

Forces acting at angles are most effectively analyzed by breaking them down into horizontal and vertical components. This process, known as vector resolution, uses trigonometric functions to resolve a single force into parts, allowing the equilibrium conditions to be applied along each axis independently.

Direction Change of the String (via Pegs or Pulleys)

When a string changes direction—such as when it passes over a smooth peg or pulley—the geometry of the situation often leads to different components of the tension acting in different directions. Although the magnitude of the tension remains constant in an ideal, frictionless system, the orientation of the string results in distinct horizontal and vertical force components that must be analyzed separately.

Transcript

Please give Ace some feedback