Question

Three identical thin rods each of length l and mass m are welded

Answer 1

for the simplicity let us assume that the rods are thin with the radius much less than L, junction of

the rods as the origin of the coordinates and the axis of rotation as the z axis

for the rod along the y axis we get

I = (1 / 3) m L2

for the rod parallel to the z axis the parallel axis theorem gives

I = (1 / 2) m r2 + m (L / 2)2

= (1 / 4) m L2

in the rod we can see that along the x axis the bit of the material between x and x+ dx has a mass

(m / L) dx

and is at a distance

r = √[x2 + (L / 2)2] from the axis of rotation

so the total rotational inertia will be

Itotal = (1 / 3) m L2 + (1 / 4) m L2 + -L/2∫L/2 [x2 + (L2 / 4)] (m / L) dx

= (11/12)ml^2

hope this helps

and always

#BeBrainly

Answer 2

Explanation:

Three identical thin rods, each of length `L` and mass `m`, are welded perpendicular to one another as shown in figure. The assembly is rotated about an axis that passes through the end of one rod and is parallel to another. The moment of inertia of this structure about this axis is. .