    Question

# A uniform thin rod of length 10 m is placed along x- axis such that one of its ends is at the origin. The linear mass density of the rod varies with respect to distance from the end as λ=l0x, where l0 is a constant. Then the position of the centre of mass of the rod w.r.t the origin will be:

A
103 m
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
203 m
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
10 m
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
3 m
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is B 203 m Let dm be the mass of a small element of the rod of length dx at a distance x from it's end. Linear mass density λ=dmdx ⇒dm=λdx=l0x dx.....(i) Let xCM be the position of COM of the rod. Applying the basic formula and taking limits from x=0 to x=L=10 m xCM=∫xdm∫dm=∫100x(l0x)dx∫100(l0x)dx=l0∫100x2dxl0∫100xdx ⇒xCM=[x33]100[x22]100=203 m  Suggest Corrections  1      Similar questions  Related Videos   Integrating Solids into the Picture
PHYSICS
Watch in App  Explore more