Alight hollow tube of 2.00 cm diameter and 1.0 m length is filled with tiny beads of different density. the resulting density distribution is linear, with the left end having a density of 1.8 g/cm3, and the right end having a density of 9.6 g/cm3. how far from the left end will be the center of mass (give answer in cm)?

The centre of mass will be at a distance of 0.614 m from the left end of the light hollow tube.

Explanation:

Given:

Diameter of the hollow pipe= 2 cm

Length of the hollow tube=1 m

Density at the left

Density at the right end

Let the density of the tube varies as

putting the end points of density as follows we have

we get a=1.8 and

where  

We know that the x coordinate  centre of the mass  is given by

where dm is the mass of an element given by

Now we have