The figure shows two cones A and B with the conditions `h_(A)lth_(B),rho_(A)gtrho_(B)`
`R_(A)=R_(B)`,`m_(A)=m_(B)`. Identify the correct statement abut their axis of symmetry.

Options

A. both have same moment of inertia
B. a has greater moment of inertia
C. B has greater moment of inertia
D. Nothing can be said

Explanation

`(x)/(r)=(h)/(R)impliesr=(x)/(h)R`
volume of disc `=(pir^(2))dX`
Mass of disc `=(pir^(2))(dX)rho=dm`
`dI=(1)/(2)(dm)r^(2)=(1)/(2)(pir^(2)dx)rhor^(2)`
`=(pirho)/(2)r^(4)dx=((pirho)/(2))((R^(4))/(h^(4)))x^(4)dx`
`I=int_(0)^(4)dI=((pirho)/(2))((R^(4))/(h^(4)))(h^(5))/(5))`
`=((pirho)/(10))(hR^(4))`
`rho=(m)/(((1)/(3)piR^(2)h))`
`thereforeI=((pi)/(10))((m)/((1)/(3)piR^(2)h))(hR^(4))`
So, `IpropmR^(2)`
Since m and R are some therefore I is same.