Question

A uniform rope of mass 2 kg and length 1 m is placed on smooth
horizontal surface. A horizontal force 4 N is applied at its one end as
shown in figure. The tension at mid-point of the rope will be
1N
4 N
2 N
3N​

Answer 1

Given:

A uniform rope of mass 2 kg and length 1 m is placed on smooth horizontal surface. A horizontal force 4 N is applied at its one end as shown in figure.

To find:

Tension at the midpoint of the rope.

Calculation:

Let tension at midpoint be T; mass of each half will be 2/2 = 1 kg.

As per FBD of right part of rope:

$4 - T = 1a \: \: \: \: \: ......(1)$

As per FBD of left part of rope:

$T = 1a \: \: \: \: \: .....(2)$

Adding the equations:

$\therefore \: 2a = 4 \\ = > a = \dfrac{4}{2} \\ = > a = 2 \: m {s}^{ - 2}$

Now , putting value of "a" in eq.(2):

$T = 1a \: \: \: \: \: .....(2)$

$= > T = 1\times 2$

$= > T = 2 \: newton$

So, final answer is:

$\boxed{ \bf{ T = 2 \: newton}}$