Question: Suppose a peach of mass M and radius R consists of a sphericalpit of r

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Question:
Suppose a peach of mass M and radius R consists of a sphericalpit of radius 0.5 R and mass 0.05 M surrounded by a spherical shellof fruit of mass 0.95 M. What is the moment of inertia of thepeach?
The answer should be in terms of MR^2.
Also here is a hint my instructor gave us. I think i'm prettyclose to the answer I'm just not getting it. A Hint: When trying to compute the moment of inertia ofthe of the fruit shell, note that you cannot use thebook's formula for a shell (2/3*m*r2) since this is onlyapplicable for a thin shell. Here, we clearly havea thick shell where the inner and outer radii differ by alot. You must therefore calculate the moment of inertia for a thickshell of inner radius Rinnerand outer radiusRouter. To do this, consider that the differentialvolume of a shell of thickness dr is 4*pi*r2*dr. A shellof thickness dr is definitely a thin shell, so this shell will havea moment of inertia of dI = 2/3*dm*r2, where dm =(density)*(differential volume). Once you have an expression for dIyou can integrate it from Rinner toRouter. You will also need to use that the density isthe total mass divided by the total volume, and the volume of athick shell will be equal to the (Volume of a sphere of radiusRouter) - (Volume of a sphere of radiusRinner).
ANY HELP WOULD BE MUCHAPPRECIATED! THANK YOU!
Suppose a peach of mass M and radius R consists of a sphericalpit of radius 0.5 R and mass 0.05 M surrounded by a spherical shellof fruit of mass 0.95 M. What is the moment of inertia of thepeach?
The answer should be in terms of MR^2.
Also here is a hint my instructor gave us. I think i'm prettyclose to the answer I'm just not getting it. A Hint: When trying to compute the moment of inertia ofthe of the fruit shell, note that you cannot use thebook's formula for a shell (2/3*m*r2) since this is onlyapplicable for a thin shell. Here, we clearly havea thick shell where the inner and outer radii differ by alot. You must therefore calculate the moment of inertia for a thickshell of inner radius Rinnerand outer radiusRouter. To do this, consider that the differentialvolume of a shell of thickness dr is 4*pi*r2*dr. A shellof thickness dr is definitely a thin shell, so this shell will havea moment of inertia of dI = 2/3*dm*r2, where dm =(density)*(differential volume). Once you have an expression for dIyou can integrate it from Rinner toRouter. You will also need to use that the density isthe total mass divided by the total volume, and the volume of athick shell will be equal to the (Volume of a sphere of radiusRouter) - (Volume of a sphere of radiusRinner).
ANY HELP WOULD BE MUCHAPPRECIATED! THANK YOU!

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