A solid sphere is rolling on a frictionless surface, shown in figure with a translational velocity $v\,\,m/s.$ If it is to climb the inclined surface then $v$ should be
$ \ge \sqrt {\frac{{10}}{7}gh} $
$ \ge \sqrt {2gh} $
$2gh$
$\frac {10}{7}\,gh$
Two loops $P$ and $Q$ are made from a uniform wire. The radii of $P$ and $Q$ are $r_1$ and $r_2$ respectively, and their moments of inertia are $I_1$ and $I_2$ respectively. If $I_2/I_1=4$ then $\frac{{{r_2}}}{{{r_1}}}$ equals
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 $t$ :-
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
A disc of mass $M$ and radius $R$ is rolling with angular speed $\omega $ on a horizontal plane as shown. The magnitude of angular momentum of the disc about the origion $O$ 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 $= r$ )