Three thin rods each of length $L$ and mass $M$ are placed along $x, y$ and $z-$ axes is such a way that one end of each of the rods is at the origin. The moment of inertia of this system about $z-$ axis is
$\frac{{2M{L^2}}}{3}$
$\frac{{4M{L^2}}}{3}$
$\frac{{5M{L^2}}}{3}$
$\frac{{M{L^2}}}{3}$
A child is standing at one end of a long trolley moving with a speed $v$ on a smooth horizontal floor. If the child starts running towards the other end of the trolley with a speed $u,$ the centre of mass of the system (trolley + child) will move with a speed.
Figure shows a thin metallic triangular sheet $ABC.$ The mass of the sheet is $M.$ The moment of inertia of the sheet about side $AC$ is
Two rings of the same radius and mass are placed such that their centres are at a common point and their planes are perpendicular to each other. The moment of inertia of the system about an axis passing through the centre and perpendicular to the plane of one of the rings is : (mass of the ring $= m,$ radius $= r$ )
If the equation for the displacement of a particle moving on a circular path is given by:
$\theta = 2t^3 + 0.5$
Where $\theta $ is in radian and $t$ in second, then the angular velocity of the particle at $t = 2\,sec$ is $t=$ ....... $rad/sec$
Moment of inertia of a uniform annular disc of internal radius $r$ and external radius $R$ and mass $M$ about an axis through its centre and perpendicular to its plane is