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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°.
Options
mass of A > mass of B
mass of A < mass of B
mass of A = mass of B
all of three are possible.
Solution
all of three are possible
We know that
N = mg cos θ˚
fmax = μN = μmg cos θ
where N = normal reaction force
fmax = frictional force
θ = angle of inclination
μ = coefficient of friction
When the block just begins to slide, it means
mg sin θ = fmax
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 − fmax = 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.
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