Question

Consider a rope of total mass $M$ and length $L$ suspended at rest from a fixed mount. The rope has a linear mass density that varies with height as $\lambda \left(z\right)={\lambda }_0\sin (\pi z\setminus L)$, where ${\lambda }_0$ is a constant. Constant gravitational acceleration $g$ acts downward.

What is the tension force$\left(inN\right)$ at the free end of the rope?

Answer 1

As mass is the function of length and we have to find tension at the free end.
So at free end the mass will be zero and since the system is at rest then we can say
$T=mg$
and since mass is zero
$\Rightarrow T=0N$