Calculate the minimum amount of work necessary to overturn a crate of mass $100 \ kg$,first about edge $AB$,then about edge $A_1B_1$. The dimensions of the crate are given in the figure. (Assume $g = 10 \ m/s^2$) (in $J$)

$A$ disc is rolling (without slipping) on a horizontal surface. $C$ is its center and $Q$ and $P$ are two points on the disc such that $Q$ is further from the contact point $O$ than $C$,and $P$ is closer to the contact point $O$ than $C$. Let $V_P, V_Q$ and $V_C$ be the magnitudes of the velocities of points $P, Q$ and $C$ respectively,then:

Two points $A$ and $B$ on a rigid body are moving as shown in the figure. The angular velocity of the body is:

$A$ table has a heavy circular top of radius $1 \,m$ and mass $20 \,kg$ placed on four light (considered massless) legs placed symmetrically on its circumference. The maximum mass that can be kept anywhere on the table without toppling it is close to ............. $kg$.

$A$ rod of length $l$ is held vertically stationary with its lower end located at a point $P$ on a horizontal plane. When the rod is released to topple about $P$, the velocity of the upper end of the rod with which it hits the ground is

There is a rod of length $l$. The velocities of its two ends are $v_1$ and $v_2$ in opposite directions normal to the rod. The distance of the instantaneous axis of rotation from $v_1$ is: