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Question: Two rings of the same radius andmass are placed such that their centres are at a common point and th...

Two rings of the same radius andmass are placed such that their centres are at a common point and their planes are perpendicular to each other. The moment of inertia of the system about an axis passing through the centre and perpendicular to the plane of one of the rings is (mass of the ring = m and radius = r):

A

1/2mr2

B

mr2

C

3/2 mr2

D

2mr2.

Answer

3/2 mr2

Explanation

Solution

I1= M.I. of ring about its diameter = ½mR2.

I1= M.I. of ring about the axis mormal to plane and passing through centre = mR2. Two rings are placed according to figure, then

=12mR2+mR2=32mR2= \frac { 1 } { 2 } m R ^ { 2 } + m R ^ { 2 } = \frac { 3 } { 2 } m R ^ { 2 }