Two metallic spheres each 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

Question

Two metallic spheres each 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 the spheres is

TestHub · Accepted Answer

The metallic spheres will be at positions as shown in the figure.

$\begin{array}{l} T \sin θ = F = \frac{G M \times M}{L^{2}} = \frac{G M^{2}}{L^{2}} .............. (1) \end{array}$

$T \cos θ = M g ................. (2)$

divide equations $(1) & (2)$

$∴ \tan θ = \frac{G M}{g L^{2}}$

$or θ = \tan^{- 1} (\frac{G M}{g L^{2}})$

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