Question

Two spherical shells have their mass uniformly distrubuted over the spherical surface. One of the shells has a diameter of 2 meters and a mass of 1 kilogram. The other shell has a diameter of 1 meter. What must the mass m of the 1-meter shell be for both shells to have the same moment of inertia about their centers of mass? m = nothing kg

Answer 1

the mass m of the 1-meter shell = 4kg

Step-by-step explanation:

The moment of inertia of a spherical shell is given as;

I = mr²

From the question, we want the two sphere's to have the same moment of inetia: Thus,

I1 = I2

Where I1 is the moment of inertia of the first spherical shell while I2 is the moment of Inertia of the second spherical shell.

Thus;

m1•r1² = m2•r2²

Where;

m1 is mass of the first spherical shell which is 1kg

r1 is radius of first shell which is = 2/2 = 1

m2 is mass of the second spherical shell which is unknown.

r2 is radius of second shell which is = 1/2 = 0.5

Now,we are are asked to find the mass of the 1m diameter shell and in this case it's m2.

Thus, let's make m2 the subject of the formula;

m2 = m1 (r1/r2)²

Plugging in the relevant values ;

m2 = 1(1/0.5)² = 4kg

For both to have same moment of inertia, mass of 1m shell must be 4kg