A wedge with a rough groove in the shape of a quarter of a circle is kept on a smooth table (see figure). A disc is placed in the groove with a small clearance. Friction exists between groove and disc

Question

A wedge with a rough groove in the shape of a quarter of a circle is kept on a smooth table (see figure). A disc is placed in the groove with a small clearance. Friction exists between groove and disc. The wedge is moved with an acceleration $3 g$ . If disc is to remain stationary relative to groove, the coefficient of friction required can be.

TestHub · Accepted Answer

m g sin θ + f s ​ = ma cos θ f s ​ = m ( a cos θ − g sin θ ) ≤ μ ( m g cos θ + ma sin θ ) ∴ μ ≥ g + a tan θ a − g tan θ ​ = 3 ​ 1 ​ = 0.577 10 9 ​ > 0.577

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