Two identical blocks of same masses are placed on a fixed wedge as shown in figure. Coefficient of f

Question

Two identical blocks of same masses are placed on a fixed wedge as shown in figure. Coefficient of friction between all the contact surfaces is &#956;. Choose the correct alternative

Accepted Answer

F.B.D. for A block

F.B.D. for B block

for block A
mg sinθ − f₁ = ma         .........(1)
for motion w.r.t. block B
mgsinθ − μmg cosθ = ma    .........(2)
for limiting case
a = 0
and    a = b = 0
⇒    mg sinθ = μmg cosθ
μ = tanθ
θ = tan^-1 μ
for block B
mgsinθ + f₁ − f₂ = mb
for motion w.r.t wedge
f₂ = 2μmg cos θ
mgsinθ + f₁ 2μmg cosθ = mb    ..........(3)
for no relative motion between A and B block from equation (1) & (3) : a = b
2mg sinμ − 2μmg cosθ = 2ma
for limiting case a = 0
⇒     θ = tan^-1 (μ)
for motion θ tan^-1 (μ)
when block B is moving w.r.t wedge
mgsinθ + f₁ − 2μ mgcosθ = mb
But f₁ = μmg cosθ    ⇒    mg sinθ − μmg cosθ = mb
for block A
mg sinθ − µmgcosθ = ma    ⇒    a = b.

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