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Question

# Two blocks having same mass are placed on rough incline plane as shown and the coefficient of friction between A and incline is μ1=1.0 and between block B and incline is μ2=1√3. As the inclination of the plane with respect to horizontal increases. Choose the correct answers(s).

A
there is no contact force between block A and B as θ30
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B
there is no contact force between blocks A and B as θ45
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C
as μ1>μ2 both the blocks move together
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D
they starts moving at an angle θ=tan1(μ1+μ22)
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Solution

## The correct options are A there is no contact force between block A and B as θ≤30∘ C as μ1>μ2 both the blocks move together D they starts moving at an angle θ=tan−1(μ1+μ22)As θ1=tan−1(μ1)andθ2=tan−1(μ2)=45∘=30∘ ∴Ifθ<30∘,thereisnocontactforcebetweenthem. For motion to start 2mg sin θ=(μ1+μ2)mg cos θ ∴tan θ=μ1+μ22

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