A block of mass m is placed on a surface having vertical cross section given by y = x²/4. If coefficient of friction is 0.5, the maximum height above the ground at which block can be placed without slipping is:
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Question

A block of mass m is placed on a surface having vertical cross section given by y = x²/4. If coefficient of friction is 0.5, the maximum height above the ground at which block can be placed without slipping is:

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G1 Physics · Accepted Answer

For equilibrium on the surface: tanθ ≤ μ At the limiting position: tanθ = μ = 0.5 Slope of the curve: dy/dx = x/2 Therefore, x/2 = 1/2 x = 1 Given, y = x²/4 y = 1/4 m