From a solid sphere of mass $M$ and radius $R$ a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its centre and perpendicular to one of its faces is
$\frac{{4M{R^2}}}{{9\sqrt 3 \pi }}$
$\frac{{4M{R^2}}}{{3\sqrt 3 \pi }}$
$\frac{{M{R^2}}}{{32\sqrt 2 \pi }}$
$\frac{{M{R^2}}}{{16\sqrt 2 \pi }}$
In the above problem the angular velocity of the system after the particle sticks to it will be ....... $rad/s$
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 centre of mass of a body
The moment of inertia of a thin circular lamina of mass $1\,kg$ and diameter $0.2\,metre$ rotating about one of its diameter is
Two spheres are rolling with same velocity (for their $C. M.$) their ratio of kinetic energy is $2 : 1$ & radius ratio is $2 : 1$, their mass ratio will be :