Question 649: Centre of Mass and Rotational Motion

Question

Three identical spherical shells, each of mass m and radius r are placed as shown in figure. Consider an axis XX' which is touching to two shells and passing through  diameter of third shell. Moment of inertia of the system consisting of these three spherical shells about XX' axis is

Accepted Answer

Net moment of inertia of the system,
I = I
1
+ I
2
+ I
3
The moment of inertia of a shell about its diameter,
I
1
= $${2 \over 3}$$mr
2
The moment of inertia of a shell about its tangent is
given by
$${I_2} = {I_3} = {I_1} + m{r^2} = {2 \over 3}m{r^2} + m{r^2} = {5 \over 3}m{r^2}$$
$$ 	herefore $$ $$I = 2 	imes {5 \over 3}m{r^2} + {2 \over 3}m{r^2} = {{12m{r^2}} \over 3} = 4m{r^2}$$

Answer

$${{16} \over 5}m{r^2}$$

Answer

4mr
2

Answer

$${{11} \over 5}m{r^2}$$

Answer

3mr
2

Centre of Mass and Rotational Motion

Three identical spherical shells, each of mass m and radius r are placed as shown in figure. Consider an axis XX' which is touching to two shells and passing through diameter of third shell. Moment of inertia of the system consisting of these three spherical shells about XX' axis is

Choose the correct answer: