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. $ta{n}^{-1}\left[\frac{GM}{gL}\right]$
• B. $ta{n}^{-1}\left[\frac{GM}{2gL}\right]$
• C. $ta{n}^{-1}\left[\frac{GM}{g{L}^2}\right]$
• D. $ta{n}^{-1}\left[\frac{2GM}{g{L}^2}\right]$

Answer 1

Answer: (C)

$F=\frac{GM\cdot M}{L^2}$
due to mutual attraction
Gravitational force
$\theta =\text{ ? }$
distance $\approx L$ (approx)
because $\to$ Grat. Force very very less strong
$\Rightarrow T\sin \theta =F$
$\therefore T\cos \theta =Mg$
$\tan \theta =\frac{F}{Mg}$
$\therefore \tan \theta =\frac{\frac{G{M}^2}{L^2}}{Mg}$
$\Rightarrow \theta ={\tan }^{-1}\left(\frac{GM}{L^{2}g}\right)$