A rope of mass $M$ is held vertically by fixing its upper end to a rigid support. The tension in the

Question

A rope of mass $M$ is held vertically by fixing its upper end to a rigid support. The tension in the rope at a distance $X$ from the rigid support will be (Given that the length of the rope is L and acceleration due to gravity is g )\

Professor PC Thomas Classes · Answer

\ Mass of unit length $=\frac{\mathrm{M}}{\mathrm{L}}$\ Mass of $(\mathrm{L}-\mathrm{x})=\frac{\mathrm{M}}{\mathrm{L}}(\mathrm{L}-\mathrm{x})$\ At the point P there are two forces\ (1) T upwards\ (2) $\frac{\mathrm{M}}{\mathrm{L}}(\mathrm{L}-\mathrm{x}) \mathrm{g}$ downwards. The point P is in equilibrium.\ $	herefore \mathrm{T}=\frac{\mathrm{M}}{\mathrm{L}}(\mathrm{L}-\mathrm{x}) \mathrm{g}$\