Question

A rope of length $10m$ and linear mass density $4kg/m$ is lying lengthwise on a horizontal smooth table. One end of the rope is pulled horizontally by a force of $40N$. The tension in the rope at a point $4m$ from point of application of force will be

• A. $40N$
• B. $24N$
• C. $49N$
• D. $15N$

Answer 1

The correct option is B $24N$


Length of rope $=10m$
Density $=4kg/m$
Given the floor is smooth
Applied force $=40N$
(Ref image)

Let total mass of rope be $m$.
Then mass of rope $m=10\times 4=40Kg$​
The left part has a mass of $6\times 4=24Kg$, as rope is uniform.

The rope moves as a single piece.
So acceleration of rope is given by
$40=4\left(10\right)a\Rightarrow a=1$


$T$ should bring the same acceleration $a$ to $6m$ length of the wire
$T=4\left(6\right)a\Rightarrow T=24N$.