Question

The mass of the part of a metal rod that lies between its left end and a point x meters to the right is 3x^2 kg. Find the linear density when is 1 m, Where is the density the highest? The lowest?

Answer 1

Answer

6 kg/m

Step-by-step explanation:

The linear density is said to give the way the mass is changing it's position and it's a derivatives of mass m here which is differenciated with respect to x position

Given

mass m = 3x^2.

Density ρ= dm/dx =6x

Then if we substitute x=1 into above expresion we have

ρ(1) =6 Kg/m

ρ= 6Kg/m

Hence this is how fast is the mass changing at that position.