Question

A block A kept on an inclined surface just begins to slide if the inclination is 30°. The block is replaced by another block B and it is found that it just begins to slide if the inclination is 40°.
(a) mass of A > mass of B
(b) mass of A < mass of B
(c) mass of A = mass of B
(d) all of three are possible.

Answer 1

(d) all of three are possible.


We know that
N = mg cos θ˚
f_max = μN = μmg cos θ
where N = normal reaction force
f_max = frictional force
θ = angle of inclination
μ = coefficient of friction

When the block just begins to slide, it means
mg sin θ = f_max
mg sin θ ₌ μmg cos θ
μ = tan θ
and the coefficient of friction depends on the angle of inclination (θ) and does not depend on mass.

Now consider the block sliding condition:
mg sin θ − f_max = ma
mg sin θ − μmg cos θ = ma
∴ a = g(sin θ − μ cos θ)

From the above equation it is clear that acceleration does not depend on the mass but depends on θ and μ.