Home
Class 11
PHYSICS
Ler l be the moment of inertia of a uni...

Ler l be the moment of inertia of a uniform square plate about an axis AB that passes through its centre and is parallel to two of its sides. CD is a line in the plane of the plate that passes through the centre of the plate and makes an angle `theta` with AB. The moment of inertia of the plate about the axis CD is then equal to

A

`I`

B

`Isin^(2)theta`

C

`Icos^(2)theta`

D

`Icos^(2)(theta/2)`

Text Solution

Verified by Experts

The correct Answer is:
A
`A'B'_|_ AB` and `C''D'_|_CD`
From symmetry `I_(AB)=I_(A'B)` and `I_(CD)=I_(CD)`
From theorem of perpendicular axis

`I_(zz)=I_(AB)I_(A'B')=I_(CD)+I_(CD')`
`implies 2I_(AB)=2II_(CD)`
`I_(AB)=I_(CD)`
Alternative method:
The relation between `I_(AB)` and `I_(CD)` should be true for all values of `theta`
At `theta=I_(CD)=I_(AB)`
Similarly at `theta=pi/2`
`I_(CD)=I_(AB)` (By symmetry)
Keeping these things in mind, option a is correct.
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

Let I be the moment of interia of a uniform square plate about an axis AB that passses through its centre and is parallel to two its sides. CD is a line in the plane of the plate that passes through the centre of the plate and makes an angle theta with AB . The moment of inertia of the plate about the axis CD is then equal to-

The moment of inertia of a copper disc, rotating about an axis passing through its centre and perpendicular to its plane

The moment of inertia of a sphere of radius R about an axis passing through its centre is proportional to-

What is the moment of inertia of a hollow sphere about an axis passing through its centre ?

The moment of inertia of uniform rectangular plate about an axis passing through its mid-point and parallel to its length l is (b = breadth of rectangular plate)

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

The moment of inertia of a uniform rod of length 2l and mass m about an axis xy passing through its centre and inclined at an angle alpha is

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

Find moment of inertia of a uniform rectangular plate about axis zz' passing through center and perpendicular to the plane of plate, as shown in Fig.