Question

two solid spheres of different materials have the same moments of inertia about their diameters . if r1 and r2 are their radii ratio of their densities is

Answer 1

Answer:

Moment of inertia of a circular disc about an axis passing through its centre of gravity and perpendicular to its plane (central axis) is given by I = ½ mr2 .

We know that masses are same for both the discs. So we have to find the radii of the two discs. Let m be the mass and b be the thickness of both the discs.

Volume of disc 1 = mass/density = m/d1 = Area x thickness = πr12 x b

Volume of disc 2 = mass/density = m/d2 = Area x thickness = πr22 x b

r12  =   m/(πbd1 )

r22  =   m/(πbd2 )

Ratio of the M.I.s of the two discs = I1/I2 =  ½ mr12 /(½ mr22 ).

                                                          = r12  / r22  

                                                          = [m/(πbd1 )] / [m/(πbd2 )]

                                                           = d2/d1

I1 : I2 = d2 : d1