Two smooth spheres each of radius 5 cm and weight W rest one on the other inside a fixed smooth cylinder of radius 8 cm. The reactions between the spheres and the vertical side of the cylinder are:

                                                           The FBD's of A and B are:

for the horizontal equilibrium of the system (A and B):

${\mathrm{N}}_{\mathrm{AW}} = {\mathrm{N}}_{\mathrm{BW}}$ -------(l)
and by diagrams:
$\cos \mathrm{\theta } = \frac{6}{10} \Rightarrow \mathrm{\theta } = {53}^0$
applying NLM on sphere,B.
$\Rightarrow {\mathrm{N}}_{\mathrm{AB}}\sin \mathrm{\theta } = \mathrm{w}$

and ${\mathrm{N}}_{\mathrm{BW}} = {\mathrm{N}}_{\mathrm{AB}} \cos \mathrm{\theta } = \frac{\mathrm{w}}{\left({\displaystyle \frac{4}{5}}\right)}\times \frac{3}{5} = \frac{3\mathrm{w}}{4}$

so ${\mathrm{N}}_{\mathrm{AW}} = {\mathrm{N}}_{\mathrm{BW}} = \frac{3\mathrm{w}}{4}$