Hint: Apply the formula for the moment of inertia of the hollow cylinder with inner and outer radius and find out the value of the moment of inertia of the hollow cylinder and then find out the moment of inertia of a thin cylinder with some assumed radius and equate the both of the moment of inertia to find the value of the assumed radius.
We know that the moment of inertia of a hollow cylinder with inner and outer radius about its axis can be written as
I=m() Where
I is the moment of inertia of the cylinder.
The mass of the cylinder denotedby
m And the inner and outer radius are denoted by
Ri and
Ro Now we are given the inner radius of the cylinder as
10cm The outer radius of the cylinder as
20cm The moment of inertia of the hollow cylinder isgiven as I
So we can find the moment of inertia of the cylinder about its axis as
I=m() Now we have found the moment of inertia of the hollow cylinder and let us know to find the moment of inertia of a thin cylinderwith no inner and outer radius.
We know the moment of inertia of thin cylinder as :
I=mk2 Where
k is the radius of the cylinder and
I is the moment of inertia of hollow cylinder
Now we are given that the moment of inertia of the two cylinders are equal and hence we can obtain an equation as below :
I=m()=mk2 Using the above equation we can get the value of the assumed radius of the hollow cylinder as
k=√ k=5√10=16 approx Hence we have found the value of the radius of the cylinder as:
16cm