$A$ particle of mass $3m$ is projected from the ground at some angle with horizontal. The horizontal range is $R$. At the highest point of its path it breaks into two pieces $m$ and $2m$. The smaller mass comes to rest and larger mass finally falls at a distance $x$ from the point of projection where $x$ is equal to

Find the centre of mass of a uniform L-shaped lamina (a thin flat plate) with dimensions as shown. The mass of the lamina is $3 \;kg$.

In the figure one fourth part of $a$ uniform disc of radius $R$ is shown. The distance of the centre of mass of this object from centre $‘O’$ is:

A $T$ shaped object with dimensions shown in the figure, is lying a smooth floor. A force $'\vec F'$ is applied at the point $P$ parallel to $AB,$ such that the object has only the translational motion without rotation. Find the location of $P$ with respect to $C$

Four identical spheres each of mass $m$ are placed at the corners of square of side $2\,metre$. Taking the point of intersection of the diagonals as the origin, the co-ordinates of the centre of mass are

Obtain an expression for the position vector of centre of mass of a system of $n$ particles in one dimension.