Question

Seven identical coins are rigidly arranged on a flat table in the pattern shown below so that each coin touches its neighbours. Each coin is a thin disc of mass $m$ and radius $r$. Note that the moment of inertia of an individual coin about an axis passing through center and perpendicular to the plane of the coin is $\frac{m{r}^2}{2}$.
The moment of inertia of the system of seven coins about an axis that passes through the point $P$ (the center of the coin positioned directly to the right of the central coin) and perpendicular to the plane of the coins is

• A. $\frac{55}{2}m{r}^2$
• B. $\frac{127}{2}m{r}^2$
• C. $\frac{111}{2}m{r}^2$
• D. $55m{r}^2$

Answer 1

Answer: (C)

$\frac{111}{2}m{r}^2$

$I_{cm}=(\frac{m{r}^2}{2}+4m{r}^2)\times 6+\frac{m{r}^2}{2}=\frac{55m{r}^2}{2}$

Using Parallel axis theorem

$I_p=\frac{55m{r}^2}{2}+28m{r}^2=\frac{111m{r}^2}{2}$