Two particles of mass $5\, kg$ and $10\, kg$ respectively are attached to the two ends of a rigid rod of length $1\, m$ with negligible mass. The centre of mass of the system from the $5\, kg$ particle is nearly at a distance of $..........\, cm$

The centre of mass of a non uniform rod of length $L$ whose mass per unit length $\lambda $ varies as $\lambda \ =\ \frac{{k\,.\,{x^3}}}{L}$ where $k$ is a constant & $x$ is the distance of any point on rod from its one end, is at distance (from the same end)

A circular disc of radius $R$ is removed from a bigger uniform circular disc of radius $2R$ such that the circumferences of the discs coincide. The centre of mass of the new  disc is $\alpha R$ from the centre of the bigger disc. The value of $\alpha$ is

A uniform square plate abcd has a mass of $1 \,kg$. If two point masses each of $20 \,g$ are placed at the corners $b$ and $c$ as shown, then the centre of mass shifts on the line

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

A uniform thin rod $AB$ of length $L$ has linear mass density $\mu \left( x \right) = a + \frac{{bx}}{L}$ , where $x$ is measured from $A$. If the $CM$ of the rod lies at a distance of $\left( {\frac{7}{12}} \right)L$ from $A$, then $a$ and $b$ are related as