Question

Solid sphere of radius r is floating in a liquid of density p with half of its volume submerged. If the sphere is slightly pushed an released, it starts performing s.H.M. Frequency of these oscillations is

Answer 1

frequency is the number of oscillation per second. its unit is Hertz (Hz). It is also inverse of time period T. Mathematically:

                                                       f = 1/T.

In simple harmonic motion, frequency is also given by formula:

                                                        f = (1/2 pie) x square root (k/m)

p[4 x pie R³/3]g = p1[2pie R³/3]g

now 2p = p1

let it is displaced through delta x

F = - pie R²(p1) (g) (deltax)

F = -K delta x

f = (1/ 2 pie) (√k/m)

m = (4/3) pie R³p

inserting values of m and k, we get

f = (1/2 pie) √3g/2R

solution of question is also solved in image