Find the centre of mass of a semi circular plate

[Neilquintal]

1. Find the centre of mass of a semi circular plate of radius R, the density of which linearly varies with distance, 'd' at the centre to a value '2d' at the circumference.
2. X_com = (∫xdm)/M
3. I tried attempting the solution but I am not really knowing how to get dm in terms of dx

 

[SteamKing]

Since you have a semi-circular plate, why not use polar coordinates to set up your integrals for the mass and the first moment?

 

[Chestermiller]

1. Find the centre of mass of a semi circular plate of radius R, the density of which linearly varies with distance, 'd' at the centre to a value '2d' at the circumference.




2. X_com = (∫xdm)/M



3. I tried attempting the solution but I am not really knowing how to get dm in terms of dx

What is your equation for density as a function of x? What is your equation for dm as a function of x?

Chet