Answer
The magnitude of the force on the spheres from each other is $~~\sqrt{2}~mg$
Work Step by Step
The force from the bottom of the container must be equal in magnitude to the total weight of the spheres:
$F = 2mg$
The vertical component of the force on the bottom sphere from the top sphere must be equal to $~~mg$
We can find the force on the bottom sphere from the top sphere:
$F~sin~\theta = mg$
$F = \frac{mg}{sin~\theta}$
$F = \frac{mg}{sin~45^{\circ}}$
$F = \frac{mg}{1/\sqrt{2}}$
$F = \sqrt{2}~mg$
The magnitude of the force on the spheres from each other is $~~\sqrt{2}~mg$
