$A$ uniform rod of length $L$ and mass $M$ is placed along the $x$-axis with its one end at the origin. The centre of mass of the rod is located at:

The 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:

$A$ $T$-shaped object of uniform thickness and same material with dimensions shown in the figure,is lying on a smooth floor. $A$ force $\vec F$ is applied at the point $P$ parallel to $AB$,such that the object has only the translation motion without rotation. Find the location of $P$ with respect to $C$.

Consider a two-particle system with particles having masses $m_1$ and $m_2$. If the first particle is pushed towards the center of mass through a distance $d$,by what distance should the second particle be moved so as to keep the center of mass at the same position?

In carbon monoxide molecules,the carbon and the oxygen atoms are separated by a distance of $1.2 \,\mathring{A}$. The distance of the centre of mass from the carbon atom is ........ $\mathring{A}$.