Question

Two metallic sphere of mass M are suspended by two strings each of length L. The distance between the upper ends of strings is L. The angle which the strings will make with the vertical due to mutual attraction of sphere is... ( if each mass horizontally moved by a distaonce of L/4 due to mutual attraction

Answer 1

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Answer 2

Given:

Mass of the spheres  M

Length of the strings = L

Distance between the two strings = L

Distance moved by the spheres due to mutual attraction = L/4

To find:

Angle which the strings will make with the vertical.

Solution:

From the figure attached with the answer, we can see that

AB = L - (L/4 + L/4)

= L/2

The force of attraction between the two sphere F = GMM/ (L/2)^2

A force of attraction between two bodies of mass m1 and m2 with a separation r = Gm1 m2/ r^2

As seen from the FBD of the sphere,

tan α = F/ Mg

Putting the value of F, we get:

tan α= GM²/ (L/2)²Mg

tan α = 4GM/ L²g

α = tan(-1) (4GM/ L²g)

The angle which the strings will make with the vertical due to mutual attraction of sphere is tan(-1) (4GM/ L²g).