Non-uniform mass per unit area of a disc?

• Jun 30th 2008, 07:29 AM
fardeen_gen
Non-uniform mass per unit area of a disc?
The mass per unit area of a disc is changing as (x + 2)/π kg/m^2 where x is the distance from the centre. If radius of the disc is 4m then:

A)mass of disc is 224/3 kg
B)mass of disc is 122π/3 kg
C)mass per unit area at centre is 2/π kg/m^2
D)mass per unit area is zero at the centre

More than one answers are correct. Please explain how to solve these types of questions too.
• Jun 30th 2008, 07:54 AM
algebraic topology
Quote:

Originally Posted by fardeen_gen
The mass per unit area of a disc is changing as (x + 2)/π kg/m^2 where x is the distance from the centre. If radius of the disc is 4m then:

A)mass of disc is 224/3 kg
B)mass of disc is 122π/3 kg
C)mass per unit area at centre is 2/π kg/m^2
D)mass per unit area is zero at the centre

More than one answers are correct. Please explain how to solve these types of questions too.

This is similar to a problem in another thread:

http://www.mathhelpforum.com/math-he...s-density.html

For this problem, the area dA of an annulus of “infinitesimal” width dx is $\displaystyle \mathrm{d}A=2\pi x\mathrm{d}x$, so the total mass is $\displaystyle M=\int_0^4{2\pi x\left(\frac{x+2}{\pi}\right)}\,\mathrm{d}x$.