A block with a square base measuring a and height h, is placed on an inclined plane. The coefficient of friction is μ. The angle of inclination (θ) of the plane is gradually increased. The block will
A
topple before sliding if μ>ah
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B
topple before sliding if μ<ah
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C
slide before topping if μ>ah
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D
slide before topping if μ<ah
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Solution
The correct option is D slide before topping if μ<ah
For no slipping: μN=μmgcosθ≤mgsinθ ⇒μ≤tanθ
For no toppling, −→τN+−→τfs+−−→τmg=0 ⇒Nx=μNh2 ∴x=μh2≤a2 ⇒μ≤ah