A uniform rod rotates in a vertical plane about the shown axis. Angular velocity at the moment is $\omega$ . Then, force on the rod by the axis at the moment

A rigid massless rod of length $3l$ has two masses attached at each end as shown in the figure. The rod is pivoted at point $P$ on the horizontal axis. When released from the initial horizontal position, its instantaneous angular acceleration will be

A wheel of radius "rolls without slipping with a speed $v$ on a horizontal road. When it is at a point $A$ on the road a small bob of the mud separates from wheel at the highest point and touches the point $B$ on the road as shown in the figure. Then $AB$ is (g-acceleration due to gravity)

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 ratio $\frac{h_{sph}}{h_{cyl}}$ is given by:

A rod of length $50 cm$ is pivoted at one end. It is raised such that it makes an angle of ${30}^o$ from the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in $rad s^{-1}$ ) will be $\left(g=10 m{s}^{-2}\right)$