An automobile engine develops $100\ kW$ when rotating at a speed of $1800\ rev/min$.  What torque does it deliver .......... $N-m$

$A$ thin rod $AB$ is sliding between two fixed right angled surfaces. At some instant its angular velocity is $ \omega $. If $I_x$ represent moment of inertia of the rod about an axis perpendicular to the plane and passing through the point $X$ ($A, B, C$ or $D$), the kinetic energy of the rod is

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 meter stick is held vertically with one end on the floor and is allowed to fall. The speed of the other end when it hits the floor assuming that the end at the floor does not slip is ......... $m / s$ $\left(g=9.8 \,m / s ^2\right)$

A uniform disk of mass $m$ and radius $R$ rolls without slipping down an incline plane of length $l$ and inclination $\theta$. Initially the disk was at rest at the top of the incline plane. Its angular momentum about the point of contact with the inclined plane when it reaches the bottom will be equal to :-

A uniform rod of length $L$ is free to rotate in a vertical plane about a fixed horizontal axis through $B$. The rod begins rotating from rest from its unstable equilibrium position. When it has turned through an angle $\theta $ its angular velocity $\omega $ is given as