Question

A circular disc 'X' of radius 'R' made from iron plate of thickness 't' has moment of inertia 'I_x' about an axis passing through the centre of disc and perpendicular to its plane. Another disc 'Y' of radius '3R' made from an iron plate of thickness `("t"/3)` has moment of inertia 'I_y' about the s same as that of disc X. The relation between I_x and l_y is ______.

Options

• I_y = 9 I_x

• I_y = I_x

• I_y = 3 I_x

• I_y = 27 I_x

Answer 1

A circular disc 'X' of radius 'R' made from iron plate of thickness 't' has moment of inertia 'I_x' about an axis passing through the center of disc and perpendicular to its plane. Another disc 'Y' of radius '3R' made from an iron plate of thickness `("t"/3)` has moment of inertia 'I_y' about the s same as that of disc X. The relation between I_x and l_y is I_y = 27 I_x.

Explanation:

`"I"_x = ("M"_x"R"^2)/2   ...."M"_x = (pi"R"^2"t")rho`

`= (pi"R"^4"t"rho)/2`

`"I"_"y" = (3pi"R"^2"t" rho "R"^2 xx 9)/2   ..."M"_"y" = (pi 9"R"^2 "t"/3)rho`

`= (27 pi "t" rho "R"^4)/2`

`therefore 27 "I"_x = "I"_"y"`