A parabolic bowl with its bottom at origin has the shape y = x 2 20 . Here x and y are in metres. The maximum height at which a small mass m can be placed on the bowl without slipping (coefficient of static friction is 0.5 ) is

Question

A parabolic bowl with its bottom at origin has the shape y = x 2 20 . Here x and y are in metres. The maximum height at which a small mass m can be placed on the bowl without slipping (coefficient of static friction is 0.5 ) is, 2.5 m, 1.25 m, 1.0 m, 4.0 m

MARKS App · Accepted Answer

Slope, d y d x = x 10 or tan ⁡ θ = x 10 ... (i) Equilibrium of mass in horizontal direction gives the equation, μ N cos ⁡ θ = N sin ⁡ θ or tan ⁡ θ = μ = 1 2 ... (ii) From Equations. (i) and (ii) x 10 = 1 2 or x = 5 m ∴ y = x 2 20 = 25 20 = 1.25 m

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