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.
-
UP 0 DOWN 0 0 1
1 Answers
262since 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