First slide

Moment of intertia

Question

Four small spheres each of radius ‘r’ and mass ‘m’ are placed with their centres at the four corners of a square of side ‘L’. The M.I. of the system about any side of square is

Moderate

A

$\large \frac{{8m{r^2}}}{5} + m{L^2}$
B

$\large \frac{{8m{r^2}}}{5} + 2m{L^2}$
C

$\large \frac{{5m{r^2}}}{8} + m{L^2}$
D

$\large \frac{{5m{r^2}}}{8} + 2m{L^2}$

Solution

$\large I = {I_1} + {I_2} + {I_3} + {I_4}$
$\large = \frac{2}{5}m{r^2} + \frac{2}{5}m{r^2} + \left( {\frac{2}{5}m{r^2} + m{L^2}} \right) + \left( {\frac{2}{5}m{r^2} + m{L^2}} \right)$
$\large I = \frac{8}{5}m{r^2} + 2m{L^2}$

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