A thin rod of mass $m$ and length $l$ is oscillating about horizontal axis through its one end. Its maximum angular speed is $\omega $. Its centre of mass will rise upto maximum height
$\frac{1}{6}\frac{{l\,\omega }}{g}$
$\frac{1}{2}\frac{{{l^2}{\omega ^2}}}{g}$
$\frac{1}{6}\frac{{{l^2}{\omega ^2}}}{g}$
$\frac{1}{3}\frac{{{l^2}{\omega ^2}}}{g}$
A circular disc is rolling on a horizontal plane. Its total kinetic energy is $300\,J$ . ....... $J$ is its translational $K.E$
The torque of the force $\overrightarrow F = (2\hat i - 3\hat j + 4\hat k\,)N$ acting at the point $\overrightarrow {r\,} = (3\hat i + 2\hat j + 3\hat k)\,m$ about the origin be
One end of a rod of length $L=1 \,m$ is fixed to a point on the circumference of a wheel of radius $R=1 / \sqrt{3} \,m$. The other end is sliding freely along a straight channel passing through the centre $O$ of the wheel as shown in the figure below. The wheel is rotating with a constant angular velocity $\omega$ about $O$. The speed of the sliding end $P$, when $\theta=60^{\circ}$ is
A smooth uniform rod of length $L$ and mass $M$ has two identical beads of negligible size, each of mass $m$ , which can slide freely along the rod. Initially the two beads are at the centre of the rod and the system is rotating with angular velocity $\omega _0$ about its axis perpendicular to the rod and passing through its mid-point (see figure). There are no external forces. When the beads reach the ends of the rod, the angular velocity of the system is
Two loops $P$ and $Q$ are made from a uniform wire. The radii of $P$ and $Q$ are $r_1$ and $r_2$ respectively, and their moments of inertia are $I_1$ and $I_2$ respectively. If $I_2/I_1=4$ then $\frac{{{r_2}}}{{{r_1}}}$ equals