A rod of length $50\,cm$ is pivoted at one end. It is raised such that if makes an angle of $30^o$ fro the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in $rad\,s^{-1}$ ) will be $(g = 10\,ms^{-2})$
$\sqrt \frac {30}{2}$
$\sqrt {30}$
$\sqrt \frac {20}{2}$
$ \frac {\sqrt {30}}{2}$
A thin uniform rod of length $2\,m$. cross sectional area ' $A$ ' and density ' $d$ ' is rotated about an axis passing through the centre and perpendicular to its length with angular velocity $\omega$. If value of $\omega$ in terms of its rotational kinetic energy $E$ is $\sqrt{\frac{\alpha E}{ Ad }}$ then the value of $\alpha$ is $...........$
A smooth tube of certain mass closed at both ends is rotated in a gravity free space and released. The two balls shown in figure moves towards the ends of the tube and stay there. Then which statement is incorrect about this whole system
A metal sphere of radius $r$ and specific heat $S$ is rotated about an axis passing through its centre at a speed of $f$ rotations per second. It is suddenly stopped at $50\%$ of its energy is used in increasing its temperature. Then the rise in temperature of the sphere is
To maintain a rotor at a uniform angular speed of $200 \;rad s^{-1}$, an engine needs to transmit a torque of $180 \;N m .$ What is the power required by the engine?
(Note: uniform angular velocity in the absence of friction implies zero torque. In practice, applied torque is needed to counter frictional torque). Assume that the engine is $100 \%$ efficient.
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