Question

30.
44. A uniform rope of length 5m is on a smooth
horizontal surface. It is being pulled by a
horizontal force of 20 N at one end. The ratio
of tension at a distance of 2m from force end
to tension at a distance of 2m from free end is,
1) 1:1
2) 2:3
3) 1:2
4) 3:2

Answer 1

Since, the length of the rope is L let at point x a small tension is given in a direction opposite to the acceleration of the rope.

For x length of rope = Mx/L.

Again, F-T=(M/L - x)(F/M).

F-T=Fx/L.

So, tension T = F-Fx/L.

Tension = F(L-x)/L .

Tension T1:

= 20(5 - 2)/5

= 12N

Tension T2:

= 20(5 - 3)/5

= 8N

Now,

Ratio = T1/T2

         = 12/8

         = 3 : 2

Hope it helps!