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A UNIFORM ROPE IS MOVING WITH ACONSTANT ACCELERATION ON A SMOOTH HORIZONTAL SURFACE. WHAT IS THE RATIO OF THE TENSION IN ROPE AT ITS MIDPOINT TO THE APPLIED FORCE AT ONE END?

abhinavabcd

learner

how do you get that ?

i was under the impression that tension would be absent if there is no load on the other end....appears i was grossly wrong...someone explain it please

aditya_arora04

Well, the answer 1:2 is correct.

At the mid point, Let tension be T, force applied be F, and a be acceleration.

So, after drawing FBD, we get :

F-T=ma/2 [ we take mass as m/2 because, the net force on mid point is same

as the part of rope where the force F acts i.e mass of rope is m/2 ]

We know, F=ma

So, T is ma/2 at mid-point

So ratio is :

T:F = 1:2

learner

Ok ...thanks!!

m.mannattil

Let the force applied be F. Then, acceleration of the rope is F/m. Since the rope is uniform, the force acting on the mid-point will be 1/2 m * F/m = F/2. Hence, ratio is 1:2

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