A wheel of radius $r$ rolls without slipping with a speed $v$ on a horizontal road. When it is at a point $A$ on the road, a small jump of mud separates from the wheel at its highest point $B$ and drops at point $C$ on the road. The distance $AC$ will be
$\upsilon \sqrt {\frac{r}{g}} $
$2\upsilon \sqrt {\frac{r}{g}} $
$4\upsilon \sqrt {\frac{r}{g}} $
$\upsilon \sqrt {\frac{3r}{g}} $
The force $7\hat i + 3\hat j - 5\hat k$ acts on a particle whose position vector is $\hat i - \hat j + \hat k$. What is the torque of a given force about the origin ?
We have two spheres, one of which is hollow shell and the other solid. They have identical masses and moment of inertia about their respective diameters. The ratio of their radius is given by
The moment of inertia of a uniform thin rod of length $L$ and mass $M$ about an axis passing through the rod from a point at a distance of $L/3$ from one of its ends perpendicular to the rod is
If a solid sphere is rolling, the ratio of its rotational energy to the total kinetic energy is given by
A solid cylinder of mass $M$ and radius $R$ rolls without slipping down an inclined plane making an angle $\theta $ with the horizontal. then its acceleration is