Question

A body of mass $M$ is hanging by an inextensible string of mass $m$. If the free end of the string accelerates up with constant acceleration $a$, find the variation of tension in the string as a function of the distance measured from the mass $M$ (bottom of the string).

Answer 1

T = (M + \frac{mx}{l})(g+a)

Answer 2

The tension at any point $x$ from the bottom of the string supports the mass $M$ and the portion of the string of length $x$ below that point, while also providing the net force required to accelerate this combined mass upwards. By applying Newton's second law to the system consisting of mass $M$ and the string segment of length $x$, considering the upward tension $T$, and the downward weights of $M$ and the string segment, we derive the expression for tension.

The final answer is $T = \left(M + \frac{mx}{l}\right)(g+a)$.