The maximum tension which an inextensible ring of mass $0.1\, kg/m$ can bear is $10\,N$. The maximum velocity in $m/s$ with which it can be rotated is ........ $m/s.$
$10$
$\sqrt {10}$
$20$
$15$
An annular ring with inner and outer radii $R_{1}$ and $R_{2}$ is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring, $\frac{F_{1}}{F_{2}}$ is
At time $t=0$, a disk of radius $1 m$ starts to roll without slipping on a horizontal plane with an angular acceleration of $\alpha=\frac{2}{3} rad s ^{-2}$. A small stone is stuck to the disk. At $t=0$, it is at the contact point of the disk and the plane. Later, at time $t=\sqrt{\pi} s$, the stone detaches itself and flies off tangentially from the disk. The maximum height (in $m$ ) reached by the stone measured from the plane is $\frac{1}{2}+\frac{x}{10}$. The value of $x$ is. . . . . . .[Take $g=10 m s ^{-2}$.]
A car sometimes overturns while taking a turn. When it overturns, it is
Defined a vehicle can be parked on a slope.
A train runs along an unbanked circular track of radius $30 \;m$ at a speed of $54\; km / h$ The mass of the train is $10^{6}\; kg$. What provides the centripetal force required for this purpose - The engine or the rails? What is the angle of banking required to prevent wearing out of the rail?