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

vapour or gas assuming atmospheriv pressure

c. newton's third law of motion