Question

If 27 small spheres each of MI. I about their diametrical axis are combined to form a big sphere,then the MI of the big sphere about its diameter is

Answer 1

Answer:243 MI

Explanation:

Given 27 small sphere combined to form a big sphere

Moment of inertia of each small sphere is MI

Let m be the mass of small sphere

therefore mass of big sphere is 27 m

thus $M=27 m$

$M=\rho \frac{4\pi R^3}{3}$

$m=\rho \frac{4\pi r^3}{3}$

where R and r is the radius of big and small sphere

thus $R=3r$

moment of inertia of small sphere

$MI=\frac{2mr^2}{5}$

moment of inertia of big sphere

$MI '=\frac{2\times 27m\times (3r)^2}{5}$

$MI'=243 MI$

Answer 2

Answer:

27 I

Explanation:

We are given that

Moment of inertia of each sphere about their diametrical axis =I

Total number of spheres=27

We have to find the moment of inertia of the big sphere about its diameter.

Mass of new sphere=27  units

Then, moment of inertia of big about its diameter=$27\times I$

Therefore,moment of inertia of big about its diameter=27 I

Answer: 27 I