Question

Three identical uniform rods of the same mass M and length L are arranged in xy plane.A fourth uniform rod of mass 3M has been placed as shown in the xy plane.What should be the value of the length of the fourth rod such that the centre of mass. of all the four rods lie at the origin?

Answer 1

Explanation:

The moment of inertia of a single rod about an axis passing through its center and perpendicular to it is

1

12

M

L

2

That of each side of the equilateral triangle about an axis passing through the triangle's center and perpendicular to its plane is

1

12

M

L

2

+

M

(

L

2

√

3

)

2

=

1

6

M

L

2

(by the parallel axis theorem).

The moment of inertia of the triangle about this axis is then

3

×

1

6

M

L

2

=

1

2

M

L

2

Answer 2

Answer:

Explanation:here is the answer of the given question