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

`l_1 + l_2`

B

`l_3 + l_4`

C

`l_1 + l_3`

D

`l_1 + l_2 + l_3 + l_4`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
(a,b,c) To find the moment of inertia of ABCD about an axis
passing through the centre O and perpendiuclar to the plane
of the plate, 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`
Also, `I_(zz)` = `I_3` +`I_4`
Adding (i) and (ii),
`2I_(zz`) = I_1 + I_2 + I_3 +I_4`
But `I_2 = I_2 and I_3 = I_4`
(By symmetry)
`:. 2I_(zz') = I_1 + I_1 + I_3 + I_3`
`=2l_1 + 2l_3`
`rArr I_(zz') = I_1 + I_3.`
.
Promotional Banner

Topper's Solved these Questions

  • ROTATIONAL MOTION

    SUNIL BATRA (41 YEARS IITJEE PHYSICS)|Exercise MCQs with one correct answer|1 Videos

  • MOTION

    SUNIL BATRA (41 YEARS IITJEE PHYSICS)|Exercise JEE Main And Advanced|63 Videos

  • SIMPLE HARMONIC MOTION

    SUNIL BATRA (41 YEARS IITJEE PHYSICS)|Exercise JEE Main And Advanced|69 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