A circular disc of radius $R$ has a uniform thickness. A circular hole of diameter equal to the radius of disc has been cut out as shown. Distance of centre of mass of the remaining disc from point $O$ is
$\frac{R}{14}$
$\frac{R}{12}$
$\frac{R}{8}$
$\frac{R}{6}$
Five masses each of $2\, kg$ are placed on a horizontal circular disc, which can be rotated about a vertical axis passing through its centre and all the masses be equidistant from the axis and at a distance of $10\, cm$ from it. The moment of inertia of the whole system (in $gm-cm^2$) is (Assume disc is of negligible mass)
The moment of inertia of a sphere (mass $M$ and radius $R$) about it’s diameter is $I$. Four such spheres are arranged as shown in the figure. The moment of inertia of the system about axis $XX'$ will be
A cockroach of mass $\frac {M}{2}$ is start moving, with velocity $V$ on the circumference of a disc of mass $'M'$ and $'R',$ what will be angular velocity of disc?
A solid cylinder of mass $M$ and radius $R$ rolls without slipping down an inclined plane of length $L$ and height $h$. What is the speed of its centre of mass when the cylinder reaches its bottom
The mass per unit length of a rod of length $l$ is given by : $\lambda = \frac{M_0x}{l}$ ,where $M_0$ is a constant and $x$ is the distance from one end of the rod. The position of centre of mass of the rod is