A thin uniform rod of length $l$ and mass $m$ is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is $\omega $. Its centre of mass rises to a maximum height of
$\frac{1}{3}\frac{{{l^2}{\omega ^2}}}{g}$
$\frac{1}{6}\frac{{{l\omega}}}{g}$
$\frac{1}{2}\frac{{{l^2}{\omega ^2}}}{g}$
$\frac{1}{6}\frac{{{l^2}{\omega ^2}}}{g}$
An energy of $484\,J$ is spent in increasing the speed of a flywheel from $60\,rpm$ to $360\,rpm$. The moment of inertia of the flywheel is $.............\,kg - m ^2$
The grinding stone of a flour mill is rotating at $600\, rad/sec$. for this power of $1.2\, k\, watt$ is used. the effective torque on stone in $N-m$ will be
A solid circular disc of mass $50 \mathrm{~kg}$ rolls along a horizontal floor so that its center of mass has a speed of $0.4 \mathrm{~m} / \mathrm{s}$. The absolute value of work done on the disc to stop it is____ $\mathrm{J}$.
A solid sphere of mass $1\ kg$ rolls on a table with linear speed $1\ m/s$. Its total kinetic energy is .......... $J$
Two bodies have their moments of inertia $I$ and $2 I$ respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular momentum will be in the ratio