Home
Class 11
PHYSICS
The moment of inertia of a thin square p...

The moment of inertia of a thin square plate ABCD, fig, of uniform thickness about an axis passing through the centre O and perpendicular to the plane of the plate is
where `l_1, l_2, l_3 and l_4` are respectively the moments of intertial about axis 1,2,3 and 4 which are in the plane of the plate.

A

`I_(1)+I_(2)`

B

`I_(3)+I_(4)`

C

`I_1+I_3`

D

`I_(1)+I_(2)+I_(3)+I_(4)`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
To find the moment of inertia of `ABCD` about an axis passing through centre `O` and perpendicular the the plane of the plane we use perpendicular axis theorem. If we consider `ABCD` to be in the `X-Y`-plane, then we know that

`I_(zz')=I_("xx"')+I_(yy')`
`:. I_(zz')=I_(1)+I_(2)`.........i
Also `I_(zz')=I_(3)+I_(4)`.........ii
Adding eqn i and ii we get
`2I_(zz')=I_(1)+I_(2)+I_(3)+I_(4)`
But `I_(1)=I_(2)` and `I_(3)=I_(4)` (by symmetry)
`:. 2I_(zz')=I_(1)+I_(1)+I_(3)+I_(3)`
`=2I_(I)1+2I_(3)`
Promotional Banner

Topper's Solved these Questions

  • RIGID BODY DYNAMICS 2

    CENGAGE PHYSICS|Exercise AR_TYPE|2 Videos

  • RIGID BODY DYNAMICS 2

    CENGAGE PHYSICS|Exercise LC_TYPE|8 Videos

  • RIGID BODY DYNAMICS 2

    CENGAGE PHYSICS|Exercise SCQ_TYPE|29 Videos

  • RIGID BODY DYNAMICS 1

    CENGAGE PHYSICS|Exercise Integer|11 Videos

  • SOUND WAVES AND DOPPLER EFFECT

    CENGAGE PHYSICS|Exercise Integer|16 Videos

Similar Questions

Explore conceptually related problems

The moment of inertia of a thin square plate ABCD of uniform thickness about an axis passing through its center and perpendicular to its plane will

The moment of inertia of a thin square plate ABCD of uniform thickness about an axis passing through the centre O and perpendicular to the plane of the plate is (a) I_(1)+I_(2) , (b) I_(2)+I_(4) 2I_(1)+I_(3) , (d) I_(1)+2I_(3)

The moment of inertia of a square plate of mass 4kg and side 1m about an axis passing through its centre and perpendicular to its plane is

What is the moment of inertia of a triangular plate ABC of mass M and side BC='a' about a axis passing through A and perpedicular to the plane of the plate?

Moment of inertia of a square plate of side l about the axis passing through one of the corner and perpendicular to the plane of square plate is given by :

Derive an expression for moment of inertia of a thin circular ring about an axis passing through its centre and perpendicular to the plane of the ring.

Find the moment of inertia of a uniform square plate of mass M and edge of length 'l' about its axis passing through P and perpendicular to it.

Moment of inertia of a thin rod of mass m and length l about an axis passing through a point l/4 from one end and perpendicular to the rod is