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Two discs of same mass and same thickness have densities as 7gm/cm cube and 51 gm/cm cube.The ratio of thier moment of inertia about their central axes is what?????

Two discs of same mass and same thickness have densities as 7gm/cm cube and 51 gm/cm cube.The ratio of thier moment of inertia about their central axes is what?????

Grade:11

1 Answers

Arun
25750 Points
6 years ago
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
 
Hence I1 : I2 = 51 :3
 

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