# Mass of thin lamina

1. Oct 30, 2016

1. The problem statement, all variables and given/known data
A plate is in the form of half disc of radius a and placed at positive y-axis. Given that the density of plate is directly proportional to the distance of the straight edge of the plate . Find the mass

2. Relevant equations

3. The attempt at a solution
$$\int_{0}^\pi \int_{0}^a\ kyr \, dr \, d\theta$$

i gt the ans is 2k(a^3)/3 , but the ans is k(a^3)/3

P/s : density is directly proportional to ky

#### Attached Files:

• ###### 423.png
File size:
1.7 KB
Views:
23
Last edited: Oct 30, 2016
2. Oct 30, 2016

### Jonathan Scott

You don't seem to have anything in there to represent the fact that $y$ describes a half disc. You could for example define $y$ as a function of $x$, or convert to polar coordinates and define $y$ as a function of $r$ and $\theta$.

3. Oct 30, 2016

### Staff: Mentor

The limits of integration of the polar integral show that the region of integration is a half circle.
I get the same answer as you do, so either we have both made the same mistake, or there is an error in the book's answer.

In your integral above, you show y in the integrand. I assume that you changed this to $r\sin \theta$ in your work.

4. Oct 30, 2016