A ball is thrown on a lawn in such a way that it initially slides with a speed $v_0$ without rolling. It gradually picks up rotation motion. Find the speed of the ball at which there will be rolling without slipping-
$\frac{2}{7}\, v_0$
$\frac{2}{5}\, v_0$
$\frac{5}{7}\, v_0$
$\frac{3}{5}\, v_0$
A $T-$ shaped object of uniform thickness and same material with dimensions shown in the figure, is lying on a smooth floor. A force $\vec F$ is applied at the point $P$ parallel to $AB,$ such that the object has only the translation motion without rotation. Find the location of $P$ with respect to $C$
A tube of length $L$ is filled completely with an incompressible liquid of mass $M$ and closed at both the ends. The tube is then rotated in a horizontal plane about one of its end with a uniform angular velocity $\omega $. The force exerted by the liquid at the other end is
If the angular momentum of a body is increased by $200\,\%$ then increase in its rotational kinetic energy will be ....... $\%$.
If a solid sphere is rolling, the ratio of its rotational energy to the total kinetic energy is given by
The plank in the figure moves a distance $100\,mm$ to the right while the centre of mass of the sphere of radius $150\, mm$ moves a distance $75\,mm$ to the left. The angular displacement of the sphere (in radian) is (there is no slipping anywhere) :-