A narrow but tall cabin is falling freely near the earth's surface. Inside the cabin, two small stones $A$ and $B$ are released from rest (relative to the cabin). Initially $A$ is much above the centre of mass and $B$ much below the centre of mass of the cabin. A close observation of the motion of $A$ and $B$ will reveal that
both $A$ and $B$ continue to be exactly at rest relative to the cabin
$A$ moves slowly upward and $B$ moves slowly downward relative to the cabin
both $A$ and $B$ fall to the bottom of the cabin with constant acceleration due to gravity
$A$ and $B$ move slightly towards each other vertically
A circular plate of uniform thickness has diameter $56\ cm$. A circular part of diameter $42\ cm$ is removed from one edge. What is the position of the centre of mass of the remaining part ........ $cm$.
Four particle of masses $m, 2m, 3m$ and $4m$ are arranged at the corners of a parallelogram with each side equal to $a$ and one of the angle between two adjacent sides is $60^o$. The parallelogram lies in the $x-y$ plane with mass m at the origin and $4m$ on the $x-$ axis. The centre of mass of the arrangement will be located at
The position of the centre of mass of a cube of uniform density will be at
A spherical hollow is made in a lead sphere of radius $R,$ such that its surface touches the outside surface of lead sphere and passes through the centre. What is the shift in the centre of mass of lead sphere due to the following ?
Distance of the centre of mass of a solid uniform cone from its vertex is $z_0$ . If the radius of its base is $R$ and its height is $h$ then $z_0$ is equal to