Look at the drawing given in the figure which has been drawn with ink of uniform line-thickness. The mass of ink used to draw each of the two inner circles, and each of the two line segments is $m$. The mass of the ink used to draw the outer circle is $6 \mathrm{~m}$. The coordinates of the centres of the different parts are: outer circle $(0,0)$, left inner circle $(-a, a)$, right inner circle $(a, a)$, vertical line $(0,0)$ and horizontal line $(0,-a)$. The $y$-coordinate of the centre of mass of the ink in this drawing is

The position vector of the centre of mass $\vec r\, cm$ of an asymmetric uniform bar of negligible area of cross-section as shown in figure is

The $(x -y)$ co-ordinates $(in\ cm)$ of the centre of mass of letter $E$ relative to the origin $O$ , whose dimensions are shown in the figure is :
(Take width of the letter $2\ cm$ every where) :

A uniform square wooden sheet of side $a$ has its centre of mass located at point $O$ as shown in the figure below on the left. A square portion of side $b$ of this sheet is cut out to produce an $L$-shaped sheet as shown in the figure on the right.The centre of mass of the L-shaped sheet lies at the point $P$ (in the above diagram), when

A stick has its bottom end attached to a wall by a pivot and is held up by a massless string attached to its other end. Which of the following scenarios has the smallest tension in the string ? (Length of stick is same in all scenarios)

The centre of mass of a body