A constant power is supplied to a rotating disc. Angular velocity $\left( \omega \right)$ of disc varies with number of rotations $(n)$ made by the disc as
$\omega \propto {\left( n \right)^{1/3}}$
$\omega \propto {\left( n \right)^{3/2}}$
$\omega \propto {\left( n \right)^{2/3}}$
$\omega \propto {\left( n \right)^2}$
$A$ ring of mass $m$ is rolling without slipping with linear velocity $v$ as shown is figure. $A$ rod of identical mass is fixed along one of its diameter. The total kinetic energy of the system is :-
Rotational kinetic energy of a given body about an axis is proportional to
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
The speed of a homogeneous solid sphere after rolling down an inclined plane of vertical height $h$, from rest without sliding, is
$A$ ring of mass $m$ and radius $R$ has three particles attached to the ring as shown in the figure. The centre of the ring has a speed $v_0$. The kinetic energy of the system is: (Slipping is absent)