Question

A thin rod of mass m and length l has variable linear density given by

Answer 1

Answer

b) the mass is

fAxdx from oto L

a)

The center of mass is

com = {x*Ax dx / {Ax dxfromotolL

com = A/3*LA3/ A/2*LA2

com = 2/3*L (from left end)

_______

below.

U=∫gh(x)(dmdx)dx

h(x)=xtanθ

dmdx=mL

then

U=gmLtanθ∫h(x)dx=(12gmLtanθ)(Lcosθ)2

or

U=12(gmL)sinθcosθ