A solid cylinder rolls without slipping down an inclined plane of height $h$. The velocity of the cylinder when it reaches the bottom is
$\sqrt {\frac{{2gh}}{3}} $
$\sqrt {\frac{{4gh}}{3}} $
$\sqrt {\frac{{3gh}}{2}} $
$\sqrt {gh} $
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
Two discs of moments of inertia $I_1$ and $I_2$ about their respective axes (normal to the disc and passing through the centre), and rotating with angular speed $\omega _1$ and $\omega _2$ are brought into contact face to face with their axes of rotation coincident. What is the loss in kinetic energy of the system in the process?
Figure shows a thin metallic triangular sheet $ABC.$ The mass of the sheet is $M.$ The moment of inertia of the sheet about side $AC$ is
$A$ car travelling on a smooth road passes through $a$ curved portion of the road in form of an arc of circle of radius $10 m$. If the mass of car is $500\, kg$, the reaction on car at lowest point $P$ where its speed is $20 m/s$ is ......... $kN$.
$ ABC$ is a triangular plate of uniform thickness. The sides are in the ratio shown in the figure. $I_{AB}, I_{BC}, I_{CA}$ are the moment of inertia of the plate about $AB, BC$ and $CA$ respectively. Which one of the following relations is correct