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Question

A block of mass m is placed on a surface 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
  1. 16 m
  2. 23 m
  3. 13 m
  4. 12 m


Solution

The correct option is A 16 m
At equilibrium for limiting value of friction, μ=tanθ

From the question,
y=x36
tanθ=dydx=x22 
μ=x22 


Given μ=0.5
0.5=x22
x=1

Therefore, maximum vertical height for no slipping y=x36=16m

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