Find the location of the center of mass for a one-dimensional rod of length L and of linear density ë(x) = cx, where c is a constant. (Hint: You will need to calculate the mass in terms of c and L. Use any variable or symbol stated above as necessary.)

Question

X =

Answer 1

total mass*cm=INT density*x*dx=int cx2 cx= 1/3 c x^3= 1/3 cL^3

but total mass= INT denstiy dx= 1/2 cL^2

cm= 2/3 L measured from the low mass end.