1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Mass of thin lamina

  1. Oct 30, 2016 #1
    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
      423.png
      File size:
      1.7 KB
      Views:
      23
    Last edited: Oct 30, 2016
  2. jcsd
  3. Oct 30, 2016 #2

    Jonathan Scott

    User Avatar
    Gold Member

    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##.
     
  4. Oct 30, 2016 #3

    Mark44

    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.
     
  5. Oct 30, 2016 #4
    Yes , I use X = R cos theta , and y = r sin theta
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Mass of thin lamina
Loading...