frequency

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.

1 Answers

262
Aditya Bhutra ·

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

Fg = (P/2)*4/3*pi*R3 *g

let the displacement be x
considering x as very small ,

FB = P*Vsubmerged = P*g*(2/3*pi*R3 + pi*R2 *x)

Fnet = FB - Fg = 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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