A disc is rotating with angular velocity $\vec{\omega}$. A force $\vec{F}$ acts at a point whose position vector with respect to the axis of rotation is $\vec{r}$. The power associated with torque due to the force is given by ..........
$(\vec{r} \times \vec{F}) \cdot \vec{\omega}$
$(\vec{r} \times \vec{F}) \times \vec{\omega}$
$\vec{r} \times(\vec{F}, \vec{\omega})$
$\vec{r} \cdot(\vec{F} \times \vec{\omega})$
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 solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights $h_{sph}$ and $h_{cyl}$ on the incline. The radio $\frac{{{h_{sph}}}}{{{h_{cyl}}}}$ is given by
A particle performs uniform circular motion with an angular momentum $L.$ If the angular frequency of the particle is doubled and kinetic energy is halved, its angular momentum becomes
A flywheel of moment of inertia $0.32\ kg-m^2$ is rotated steadily at $120\,rad/\sec $ by a $50\,W$ electric motor. The kinetic energy of the flywheel is.......... $J$
$A$ uniform rod of mass $m$ and length $l$ hinged at its end is released from rest when it is in the horizontal position. The normal reaction at the hinge when the rod becomes vertical is :