A uniform glass rod having a length L is placed in the smooth hemispherical bowl having a radius r. Determine the angle of inclination ? for equilibrium.

Question

Robert · Accepted Answer

Note that Φ = θ 
(L – 2rcos Φ) (L – 2rcos Φ)x(cos Φ)/2 = (2rcos Φ) (2rcos Φ)x(cos Φ)/2 
 (L – 2rcos Φ) (L – 2rcos Φ) = (2rcos Φ) (2rcos Φ) 
 (L – 2rcos Φ) = (2rcos Φ) 
 cos Φ = L/4r 
 Φ = cos-1 (L/4r)

A uniform glass rod having a length L is placed in the smooth hemispherical bowl having a radius r. Determine the angle of inclination ? for equilibrium.

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