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

• A. $t a n^{- 1}\left[\frac{G M}{g L}\right] \, \, $
• B. $t a n^{- 1}\left[\frac{G M}{2 g L}\right]$
• C. $t a n^{- 1}\left[\frac{G M}{g L^{2}}\right]$
• D. $t a n^{- 1}\left[\frac{2 G M}{g L^{2}}\right]$

Answer 1

Answer: (C)

Gravity, or gravitation, is a natural phenomenon by which all things with mass or energy - including planets, stars, galaxies, and even light - are attracted to one another. On Earth, gravity gives weight to physical objects, and the Moon's gravity causes the tides of the oceans. The metallic spheres will be at positions as shown in the figure.


$Tsin \theta = F = \frac{G M \times M}{L^{2}}$
$ \, =\frac{G M^{2}}{L^{2}}$
$ \, \, Tcos \theta = M g$
$\therefore \, \, tan \theta = \frac{G M}{g L^{2}}$
$or \, \, \theta =\left(t a n\right)^{- 1}\left(\frac{G M}{g L^{2}}\right)$