A rod of length $1\,meter$ is standing vertically, when its other end touches the ground without slipping then the speed of other end will be
$\sqrt {19\times 6}\,m/sec$
$\sqrt {29\times 4}\,m/sec$
$\sqrt {9.8\times 3}\,m/sec$
$9·8\, m/sec$
Two identical circular loops are moving with same kinetic energy one rolls $\&$ other slides. The ratio of their speed is
A cord is wound round the circumference of wheel of radius $r$. The axis of the wheel is horizontal and moment of inertia about it is $I$. A weight $mg$ is attached to the end of the cord and falls from rest. After falling through a distance $h$, the angular velocity of the wheel will be
A rod of length $l$ is hinged from one end. It is brought to a horizontal position and released. The angular velocity of the rod when it is in the vertical position is
A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy $(K_t)$ as well as rotational kinetic energy $(K_r)$ simultaneously. The ratio $K_t : (K_t + K_r)$ for the sphere is
A sphere of mass $50\,gm$ and diameter $20\,cm$ rolls without slipping with a velocity of $5\,cm/sec$ . Its total kinetic energy is