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 circular hole of radius $\left(\frac{ a }{2}\right)$ is cut out of a circular disc of radius $'a'$ as shown in figure. The centroid of the remaining circular portion with respect to point $'O'$ will be :

Write short note on centre of Gravity. 

From the homogeneous square plate we cut a triangle (Figure). Side of the square is $a$ and. the apex of the triangle is at the center of the square. Distance fiom the center of the square to the center of mass of the remainder of the plate is

A circular plate of diameter ' $a$ ' is kept in contact with a square plate of side $a$ as shown. The density of the material and the thickness are same everywhere. The centre of mass of composite system will be ...........

Particles of masses $m, 2m, 3m,......nm$ $grams$ are placed on the same line at distances $l, 2l, 3l,....nl\, cm$ from a fixed point. The distance of centre of mass of the particles from the fixed point in centimetres is