A uniform rod of mass $m$ and length $l$ rotates in a horizontal plane with an angular velocity $\omega $ about a vertical axis passing through one end. The tension in the rod at a distance $x$ from the axis is
$\frac{1}{2}\,m{\omega ^2}x$
$\frac{1}{2}\,m{\omega ^2}\frac{{{x^2}}}{l}$
$\frac{1}{2}\,m{\omega ^2}l\,\left( {1 - \frac{x}{l}} \right)$
$\frac{1}{2}\,\frac{{m{\omega ^2}}}{l}\,\left( {{l^2} - {x^2}} \right)$
When helical gear $M$ turns as shown, gears $I$ & $H$ turn in the following manner. Which of the following is correct ? (Assuming no slipping anywhere)
A disc is performing pure rolling on a smooth stationary surface with constant angular velocity as shown in figure. At any instant, for the lower most point of the disc -
A thin wire of length $\ell$ and mass $m$ is bent in the form of a semicircle as shown. Its moment of inertia about an axis joining its free ends will be ...........
A particle of mass $m$ moves in the $XY$ plane with a velocity $V$ along the straight line $AB$ . If the angular momentum of the particle with respect to origin $O$ is $L_A$ when it is at $A$ and $L_B$ when it is at $B$ , then
A circular disk of moment of inertia $I_t$ is rotating in a horizontal plane, about its symmetry axis, with a constant angular speed ${\omega _i}$. Another disk of moment of inertia $I_b$ is dropped coaxially onto the rotating disk. Initially the second disk has zero angular speed. Eventually both the disks rotate with a constant angular speed ${\omega _f}$. The energy lost by the initially rotating disc to friction is