Question

Two metallic spheres, each of mass M, are suspended by two strings each of length L. The distance between the lower ends of the strings is L. The angle which the strings make with the vertical due to mutual attraction of the spheres is

• A. ${\tan }^{-1}\frac{2GM}{g{L}^2}$
• B. ${\tan }^{-1}\frac{GM}{gL}$
• C. ${\tan }^{-1}\frac{GM}{g{L}^2}$
• D. ${\tan }^{-1}\frac{GM}{2gL}$

Answer 1

The correct option is C ${\tan }^{-1}\frac{GM}{g{L}^2}$

$F=\frac{GM.M}{L^2}$

due to mutual attraction

Gravitational force

$\theta =?$

distance $\approx L$ (approx)

because $\to$ Grat. Force very very less strong

$\Rightarrow T\sin \theta =F$

$\therefore T\cos \theta =Mg$

$\tan \theta =\frac{F}{Mg}$

$\therefore \tan \theta =\frac{\frac{G{M}^2}{L^2}}{Mg}$

$\Rightarrow \theta ={\tan }^{-1}\left(\frac{GM}{L^{2}g}\right)$