A cylinder of mass $M$ and radius $r$ is mounted on a frictionless axle over a well. A rope of negligible mass is wrapped around the solid cylinder and a bucket of mass $m$ is suspended from the rope. The linear acceleration of the bucket will be
$a\, = \,\frac{{2mg}}{{M + 2m}}$
$a\, = \,\frac{{mg}}{{M + m}}$
$a\, = \,\frac{{mg}}{{M + 2m}}$
$a\, = \,\frac{{Mg}}{{M + 2m}}$
Radius of gyration of a body depends on
For a rolling body, the velocity of $P_1$ and $P_2$ are ${\vec v_1}$ and ${\vec v_2}$ , respectively
A sphere of diameter $r$ is cut from a sphere of radius $r$ such that the centre of mass of the remaining mass be at maximum distance from original centre; then the distance is
If a solid sphere is rolling, the ratio of its rotational energy to the total kinetic energy is given by
Three thin metal rods, each of mass $M$ and length $L$ are welded to form an equilateral triangle. The moment of inertia of the composite structure about an axis passing through the centre of mass of the structure and perpendicular to its plane is