A thin circular ring of mass $M$ and radius $R$ is rotating about its axis with a constant angular velocity $\omega $. Two objects, each of mass $m$, are attached gently to the opposite ends of a diameter of the ring. The ring rotates now with an angular velocity
$\frac{{\omega M}}{{M + m}}$
$\frac{{\omega (M - 2m)}}{{M + 2m}}$
$\frac{{\omega M}}{{M + 2m}}$
$\frac{{\omega (M + 2m)}}{M}$
A rigid body is rotating with variable angular velocity $(a -bt)$ at any instant of time $t.$ The total angle subtended by it before coming to rest will be ( $a$ and $b$ are constants)
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
A uniform solid sphere of mass $m$ and radius $r$ rolls without slipping down a inclined plane, inclined at an angle $45^o$ to the horizontal. Find the magnitude of frictional coefficient at which slipping is absent
A circular stage is free to rotate about vertical axis passing through centre. $A$ tortoise is sitting at corner of stage. Stage is provided angular velocity $\omega_0$. If tortoise start moving along one chord at constant speed with respect to stage then how the angular velocity of stage $\omega(t)$ vary with time $t$ :-
The angular momentum of a projectile projected at an angle $\theta $ with the horizontal with speed $u$ about the point of projection when it is at the highest point of its trajectory is