A problem about Moment of Inertia.?

Question

M.I. of a circle & a square are equal. If D = dia. of circle and L = length of the square. Find the ratio of D : L = ?
( here M. I . is about the centroidal axis)

Answer 1

D:L=1.141

Answer 2

M.I of a circle about its centroidal axis =(pi/64)*D^4 where D is the diameter of the circle.
M.I of a square = L^4/12
By the condition:
(pi/64)*D^4 = L^4/12

D^4/L^4=64/(pi*12)

D/L= [ 16/(pi*3) ]^1/4
or, D:L =1.141464

Answer 3

MI of circle = MI of sqaure => pi*D^4/64 = L^4/12

D^4/L^4 = 64/(12*pi) = 1.6977 => D/L = 1.1414 is the amswer
(Diameter D of the circle has to be 1.1414 times the side L of the square)

Answer 4

M.I OF CIRCLE=3.14/64 *D^4 where D is diam of circle.
M.I OF SQUARE = L^4/12
if M.I OF CIRCLE = M.I OF SQUARE then,
3.14/64 *D^4=L^4/12 after rearranging the terms we get,
D^4/L^4=1/12*64/3.14 taking fourth root the ans is
D/L=1.141.

Answer 5

L / D = (3 * pi / 16)^(1/4)

L : D = (3 * pi / 16)^(1/4) : 1

Answer 6

D:L=1.141