Question

A uniform rope of mass $M$ and length $L$ is accelerated upwards with acceleration ${}^{\prime }{a}^{\prime }$ by applying force on the topmost point. What is the tension in the rope at a distance $X$ from the lower end?

• A. $\frac{M}{L}\times a$
• B. $\frac{M}{L}X(g+a)$
• C. $\frac{M}{L}(L-X)a$
• D. None

Answer 1

The correct option is B $\frac{M}{L}X(g+a)$

We assume the tension ${}^{\prime }{T}^{\prime }$ at distance $X$ from lower end. Mass of the lower portion of length $X$ is ${}^{\prime }{m}^{\prime }$.
Since the rope is uniform, therefore mass per unit length remains same for every section.
$m=\left(\frac{M}{L}\right)X$

F.B.D of lower portion.


$T-mg=ma$
$T=m(g+a)$
$T=\frac{M}{L}X(g+a)$