Seven identical coins are rigidly arranged on a flat table in the… - Vidyadip

MCQ

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 $r$. Here note, that the moment of inertia of an individual coin about an axis passing through centre 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 centre of the coin positioned directly to the right of the central coin) and perpendicular to the plane of the coins is ..........$m r^2$

A
$\frac{55}{2}$
B
$\frac{127}{2}$
✓
$\frac{111}{2}$
D
$55$

✓

Answer

Correct option: C.

$\frac{111}{2}$

c
(c)

Moment of inertia of given configuration about an axis through point $A$ (centre of middle disc), using parallel axes theorem is

$I_A=\frac{m r^2}{2}+6\left(\frac{m r^2}{2}+m(2 r)^2\right)$

$=m r^2\left(\frac{1}{2}+\frac{6}{2}+24\right)=\frac{55}{2} m r^2$

Now, again using parallel axes theorem, moment of inertia of configuration about $P$ is

$I_P=I_A+M_{ total } \times d^2$

$=\frac{55}{2} m r^2+7 m(2 r)^2=\frac{111}{2} m r^2$

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