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Question

A block of mass m is placed on a suface with a vertical cross section given by y=x36. If the coefficient of friction is 0.5, the maximum height above the ground at which the block can be placed without slipping is:

A
13 m
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B
12 m
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C
16 m
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D
23 m
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Solution

The correct option is C 16 m

y=x36
Slope dydx=3x26=x22=tan θ
At equilibrium the frictional force will be balanced by the component of gravity acting down the incline and tangent to the point of the curve.
f=μ mg cos θ=mg sin θ
μ =tan θ
0.5=x22x=1
y=x36=16m

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