Question

Two identical solid copper spheres of radius R are placed in
contact with each other. The gravitational attraction
between them is proportional to
[Kerala PET 2005; MP PET 2013]
Go(a) R2
(b) R2
(d) R4
(c) RA​

Answer 1

$\large \fbox{ \: \sf \blue{ A}n{s}w{e}r \: \sf \underline}\\\\\hookrightarrow \sf {(d) R^{4} }$

$\Huge{\underline{\underline{\fbox{\mathfrak{Solution :-}}}}}$

$Mass\ of\ each\ sphere\ M_1 =M_2 = \rho (\dfrac{4}{3}\pi R^3) \\\\\Gravitational\ force\ between\ them\ is\ given\ by\ F = \dfrac {GM_{1}M_{2}}{(2R)^{2}} \\\\ F= \dfrac {G \times \dfrac {4}{3} \pi R^{3}\rho \times \dfrac {4}{3} \pi R^{3} \rho}{4R^{2}} = \dfrac {4}{9}\pi^{2} G \rho^{2} R^{4} \\\\So\ F \propto R^{4} .$