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

Options

A. `W//4` and `3W//4`
B. `W//4` and `W//4`
C. `3W//4` and `3W//4`
D. `W` and `W`

Answer

C

Explanation

The FBD's of `A` and `B` are:
for the horizontal equilibrium of the system (`A` and `B`)
`N_(AW)=N_(BW)`
and by diagrams: `costheta=(6)/(10)` implies `theta=53^(@)`
applying NML on sphere `B` .
implies `N_(AB)sintheta=w`
and `N_(BW)=N_(AB)costheta=(w)/(4//5)xx(3)/(5)=(3w)/(4)`
so `N_(AW)=N_(BW)=(3w)/(4)`