Three masses of $2\,kg$,$4\,kg$,and $4\,kg$ are placed at the three points $(1, 0, 0)$,$(1, 1, 0)$,and $(0, 1, 0)$ respectively. The position vector of its center of mass is:

Masses of $8 \ kg, 2 \ kg, 4 \ kg,$ and $2 \ kg$ are placed at the corners $A, B, C,$ and $D$ respectively of a square $ABCD$ with a diagonal of $80 \ cm$. The distance of the center of mass from $A$ is ....... $cm$.

Find the centre of mass of three particles at the vertices of an equilateral triangle. The masses of the particles are $100 \; g$,$150 \; g$,and $200 \; g$ respectively. Each side of the equilateral triangle is $0.5 \; m$ long.

$A$ point mass $m_A$ is connected to a point mass $m_B$ by a massless rod of length $l$ as shown in the figure. It is observed that the ratio of the moment of inertia of the system about the two axes $AA$ and $BB$,which are parallel to each other and perpendicular to the rod,is $\frac{I_{BB}}{I_{AA}} = 3$. The distance of the centre of mass of the system from the mass $m_A$ is

$(a)$ Centre of gravity $(C.G.)$ of a body is the point at which the weight of the body acts.
$(b)$ Centre of mass coincides with the centre of gravity if the earth is assumed to have an infinitely large radius.
$(c)$ To evaluate the gravitational field intensity due to any body at an external point,the entire mass of the body can be considered to be concentrated at its $C.G.$
$(d)$ The radius of gyration of any body rotating about an axis is the length of the perpendicular dropped from the $C.G.$ of the body to the axis of rotation.
Which one of the following pairs of statements is correct?

The centre of mass of two thin uniform rods of the same length $L$ but made of different materials and kept as shown in the figure can be,if the meeting point is the origin of coordinates: