How Does Rope Length Affect Tension in a Vertical Two-Mass System?

[num1cutiey]

In my Classical Mechanics class we are reviewing Newtonian Mechanics. He gave a homework assignment with a question that invloves tension and a rope.

The question is as follows

2 point-like objects, each with mass m, are connected by a massless, stretchless tope of length l. The objects are suspended vertically near the surface of the Earth, so that one object is hanging below the other, and then released. Find the tension in the rope after the objects are released. Use proper approximations to express the tension as a function of m, L, mass of the Earth M, radius of the Earth R, and gravitational constant G.

Find that is all good and dandy I used Newton's law of Gravitation so I could have the last few constants in there. But l?? Since when did the length of a massless, stretchless rope matter for tension?? Am I missing something??

 

[bel]

Since one object is closer to the Earth than another, the Earth accelerates them at different rates, hence the tension, which are the result of tidal forces. Normally, this effect is negligible near the Earth's surface, and especially since the Earth is not very massive.

 

[mjsd]

so you have 2 point source each is at a different distance from the Earth centre. so the closer one will experience a *slightly* larger force, the force imbalance should give a tiny tension to string

 

[Mattofix]

is the answer T = GMm(1/R^2 - 1/(R+L)^2) ?