A solid cylinder of mass $M$ and radius $R$ rolls without slipping down an inclined plane making an angle $\theta $ with the horizontal. then its acceleration is
$\frac{1}{3}\,g\, \sin \, \theta$
$\frac{2}{3}\,g\, \sin \, \theta$
$\frac{2}{5}\,g\, \sin \, \theta$
$\frac{2}{7}\,g\, \sin \, \theta$
A tube of length $L$ is filled completely with an incompressible liquid of mass $M$ and closed at both ends. The tube is then rotated in a horizontal plane about one of its end with a uniform angular velocity $\omega $ . Then the force exerted by the liquid at this other end is
We have two spheres, one of which is hollow shell and the other solid. They have identical masses and moment of inertia about their respective diameters. The ratio of their radius is given by
A circular disc is rolling on a horizontal plane. Its total kinetic energy is $300\, J$. ........ $J$ is its translational $K.E.$
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)
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?