Two uniform thin identical rods $AB$ and $CD$ each of mass $M$ and length $L$ are joined so as to form a cross as shown. The moment of inertia of the cross about a bisector line $EF$ is (Line $EF$ is perpendicular to $ABCD$ plane)
$\frac {ML^2}{6}$
$\frac {ML^2}{4}$
$\frac {ML^2}{12}$
$\frac {ML^2}{3}$
Two particles $A$ and $B$ initially at rest move towards each other under a mutual force of attraction. At the instant when velocity of $A$ is $v$ and that of $B$ is $2v$, the velocity of centre of mass of the system :
If the angular velocity of a merry-go-round is $60^o/sec$ and you are $3.5\,m$ from the centre of rotation, your linear velocity will be
The centre of mass of two particles lies
If the earth were to suddenly contract to $\frac{1}{n}^{th}$ of its present radius without any change in its mass then duration of the new day will be
A circular disk of moment of inertia $I_t$ is rotating in a horizontal plane, about its symmetry axis, with a constant angular speed $\omega _i$. Another disk of moment of inertia $I_b$ is dropped coaxially onto the rotating disk. Initially the second disk has zero angular speed. Eventually both the disks rotate with a constant angular speed $\omega _f$. The energy lost by the initially rotating disc to friction is