Two masses m1 and m2 are placed touching each other on an inclined plane forming an angle θ with the horizontal the coefficient of friction between the inclined plane and m1 is µ1 and that of between plane and m2 is µ2 where µ1 > µ2.(a) Find the interaction force between the two masses.(b) What is the minimum angle q at which masses start sliding.

(a)    Let R be the interaction force and F₁ and F₂ be the frictional force on m₁ and m₂, respectively.

m₁a = m₁g sin θ + R – µ₁N₁           m₂a = m₂g sinθ – R – µ₂N₂

N₁ – m₁gcosθ = 0                        N₂ – N₂ – µ₂ cosθ = 0

(b)    The two masses begin to slide just when the acceleration of m1 is not zero.

The limiting case is given by

m₁g sinθmin + R – µ₁m₁g cosθmin = 0

Using R from part (a)