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
Infinite rods of uniform mass density and length $L, L/2, L/4....$ are placed one upon another upto infinite as shown in figure. Find the $x-$ coordinate of centre of mass
The identical spheres each of mass $2 \mathrm{M}$ are placed at the corners of a right angled triangle with mutually perpendicular sides equal to $4 \mathrm{~m}$ each. Taking point of intersection of these two sides as origin, the magnitude of position vector of the centre of mass of the system is $\frac{4 \sqrt{2}}{x}$, where the value of $x$ is_____
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