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Q.

Friction between the wedge shown and the horizontal floor is sufficient to prevent the wedge from sliding. The mass of the wedge is M and its angle of inclination is θ . A small block of mass m is just placed near the top of the wedge and released. Friction coefficient between the wedge and the block is  μ  
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a

The wedge will topple for any value of m irrespective of μ .

b

If  μ>tanθ, the wedge will not topple for any value of m.

c

If  μ<tanθ, the wedge will topple for  m>M3sinθ(sinθμcosθ)

d

If  μ<tanθ, the wedge will not topple for  m>M3sinθ(sinθμcosθ)

answer is A, B.

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Detailed Solution

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Nsinθh>Mgb3+μmgcosθhcosθ

mgcosθ.sinθh>Mgb3+μmghcos2θ

3msinθ(sinθμcosθ)>M

m>M3sinθ(sinθμcosθ)

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