The moment of inertia of a ring about an axis perpendicular to its plane and passing through its center is $4 \,kg \,m^2$. Its moment of inertia about the tangent in the plane is

The figure shows three identical discs,each of mass $M$ and radius $R$. Find the moment of inertia of this system about the axis $xx'$.

$A$ uniform disc of radius $R$ lies in the $x-y$ plane with its centre at the origin. Its moment of inertia about the $z$-axis is equal to its moment of inertia about the line $y = x + c$. The value of $c$ is

$A$ thin square plate of side $4R$ has a mass $M$. Four circles of radius $R$ are cut from it as shown. Calculate the moment of inertia of the remaining part about the $z$-axis passing through the center of the square.

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 its 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 ..........$m r^2$.

$A$ rod of length $L$ consists of two halves: one half is made of copper with mass $m_c$ and the other half is made of silver with mass $m_s$. What is the moment of inertia of the rod about an axis passing through its midpoint and perpendicular to the rod?