frequency

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A SPHERE OF RADIUS 'R' IS FLOATING IN A LIQUID OF DENSITY '\rho ' WITH HALF OF ITS VOLUME SUBMERGED. IF THE SPHERE IS SLIGHTLY PUSHED AND RELEASED, IT STARTS PERFORMING S.H.M. FIND THE FREQUENCY OF THESE OSCILLATIONS.

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Aditya Bhutra ·2012-02-18 23:42:20

since half the volume is submerged at eqm. , density of sphere = rho/2 = P/2

F_g = (P/2)*4/3*pi*R³ *g

let the displacement be x
considering x as very small ,

F_B = P*V_submerged = P*g*(2/3*pi*R³ + pi*R² *x)

Fnet = F_B - F_g = P*pi*R²*x = M*w²*x (Restoring force)

putting M = (P/2)*4/3*pi*R³

w = √3g2R

f = w/2pi

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