Question

the MI of a thin uniform rod of mass M and length L.about an axis passing
though it's centre of mass & perpendicular to it's length is ML/12.findM.I.
and radius of gyration about an axis a) passing through it's one end and
perpendicular to it's length b) passing through a point midway between centre
and one end​

Answer 1

Answer:

We know, a thin uniform rod lying on the axis that is passing through its center have a moment of inertia,

I

XY

=

12

mL

2

Where,

m is the mass per unit length of the rod and L is the length of the rod.

Let us assume that the endpoint of the rod lies on the point (P,Q) and the moment of inertia at that point is I

′

.

I=

12

ML

2

M is the total mass.

By applying the parallel axis theorem, we have-

I

′

=I+M(

2

L

)

2

Since the distance from the center to the endpoint is

2

L

.

I

′

=

12

ML

2

+

4

ML

2

=ML

2

(

12

1

+

4

1

)

=ML

2

(

12

4

)

=4.(

12

ML

2

)

=4I