# A heavy block of mass M hangs in equilibrium at the end of a rope of mass m and length l connected to a ceiling . Determine the tension in the rope at a distance x from the ceiling ?

Oct 19, 2016

#### Answer:

$T \left(x\right) = g \left(M + \frac{l - x}{l} m\right)$

#### Explanation:

The Tension T is supporting

• the mass $M$ of the block

• that mass of the rope belonging to the length $l - x$. Assuming even distribution of mass along the rope, that mass is $\frac{l - x}{l} m$

This we can say that

$T \left(x\right) = g \left(M + \frac{l - x}{l} m\right)$