Question

ege-PHYS 1401 - 5 x Home Row Review - EdClub X Ch. 9 Problems & Exercises - Col X HW: Rotati Due Dates > HW: Rotational Motion Resources Suppose that there are two solid steel spheres. The second sphere has a radius twice as large as the radius of the first sphere. What is the ratio of the moments of inertia of the spheres, 12 : 1.? 32 16

Answer 1

Moment of inertia of a solid sphere about an axis passes through its center is given as -

I = (2/5)*M*R^2

Suppose, radius of the first sphere, R1 = R

So, radius of the second sphere, R2 = 2R

Then,

Moment of inertia of the first sphere, I1 = (2/5)*M*R1^2 = (2/5)*M*R^2

Moment of inertia of the second sphere, I2 = (2/5)*M*R2^2 = (2/5)*M*(2R)^2 = (2/5)*M*(4R^2)

Therefore,

I2 / I1 = [(2/5)*M*(4R^2)] / [(2/5)*M*R^2] = 4

Hence, first option is the correct answer.