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
$\frac {Ml^2}{18}$
$\frac {Ml^2}{12}$
$\frac {Ml^2}{6}$
$\frac {Ml^2}{4}$
A uniform solid sphere of mass $m$ and radius $r$ rolls without slipping down a inclined plane, inclined at an angle $45^o$ to the horizontal. Find the magnitude of frictional coefficient at which slipping is absent
If a solid sphere is rolling, the ratio of its rotational energy to the total kinetic energy is given by
In the following figure, a body of mass $m$ is tied at one end of a light string and this string and this string is wrapped around the solid cylinder of mass $M$ and radius $R$. At the moment $t = 0$ the system starts moving. If the friction is negligible, angular velocity at time $t$ would be
A thin circular ring of mass $M$ and radius $r$ is rotating about its axis with a constant angular velocity $\omega $ . Two objects each of mass $m$ are attached gently to the opposite ends of a diameter of the ring. The ring will now rotate with an angular velocity
Two racing cars of masses $m_1$ and $m_2$ are moving in circles of radii $r_1$ and $r_2$ respectively. Their speeds are such that each makes a complete circle in the same time $t$. The ratio of the angular speeds of the first to the second car is