wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If the linear mass density of a rod of length L lying along x-axis and origin at one end varies as λ=A+Bx, where A and B are constants, find the coordinates of the centre of mass.

Open in App
Solution

As rod is kept along x-axis
Hence, Ycm=0,Zcm=0
For coordinate
xcm=L0xdmL0Ldm=λ.dx=(A+Bx)dx
xcm=L0x(Ax+B)dxL0(A+Bx)dx=AL22+BL23AL+BL22=L(3A+2BL)3(2A+BL)
Here coordinates of the centre of mass are (L(3A+2BL)3(2A+BL),0,0)
1032555_1014137_ans_aa338408d9bc402c8aa9cc91e6c7a314.png

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Hooke's Law
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon