Two identical smooth disc of radius R have been placed on a frictionless table touching each other. Another circular plate is placed between them as shown in figure. The mass per unit area of each object is `sigma`, and the line joining the centers of the plate and the disc is `theta`
(a) Find the minimum horizontal force `F_(0)` that must be applied to the two discs to keep them together.
(b) Angle `theta` can be changed by changing the size of the circular plate. Find `F_(0)` when `theta rarr 0`.
[use `"cos"theta = 1 - (theta^(2))/(2)` and `"sin"theta = theta "for small" theta`]
(c) Find `F_(0)` when `theta rarr (pi)/(2)` . Explain the result .

Answer

(a) `F_(0) = (sigmapiR^(2)g(1- "cos"theta)^(2))/(2"sin"theta. "cos"theta)`
(b) `F_(0) = 0`
(c) `oo`