You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Moment of Inertia of a Rod

Let I1,I2 a...

Question

Let $I_{1}, I_{2}$ and $I_{3}$ be the moment of inertia uniform plate about axes $A O C, x D x^{'}$ and $y B y^{'}$ respectively as shown in the figure. The moment of inertia of the plate $I_{1} : I_{2} : I_{3}$ are in the ratio

1 : \frac{1}{7} : \frac{1}{7}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

1 : \frac{12}{7} : \frac{12}{7}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1 : \frac{7}{12} : \frac{7}{12}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1 : 7 : 7

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct options are
A $1 : \frac{1}{7} : \frac{1}{7}$
D $1 : 7 : 7$
$I_{1} = \frac{m a^{2}}{12}$
$I_{2} = I_{1} + m r^{2}$
$= \frac{m a^{2}}{12} + \frac{m a^{2}}{2} = \frac{7}{12} m a^{2}$
$∴ I_{1} : I_{2} = 1 : 7$

Suggest Corrections

Similar questions

Q. Let

I_{1}, I_{2}

and

I_{3}

be the moment of inertia of a uniform square plate about axes AOC,

x D x^{'}

and

y B y^{'}

respectively as shown in the figure. The moments of inertia of the plate

I_{1} : I_{2} : I_{3}

are in the ratio.

Q. Ratio of moment of inertia,

I_{1} : I_{2}

of a uniform square plate about shown axes is

A B C D

is a square plate with centre

O

. The moment of inertia of the plate about the axes

1, 2, 3

and

4

are

I_{1}, I_{2}, I_{3} & I_{4}

respectively. It follows that

The moment of inertia of thin square plate ABCD of uniform thickness about an axis passing through the centre O and perpendicular to the plane of the plate is not equal to (Given $I_{1}, I_{2}, I_{3} a n d I_{4}$ respectively, are the moments of inertia about axes 1,2,3and 4 which are in the plane of the plate)

Q. A thin square plate

A B C D

of uniform thickness is shown in the figure.

I_{1}, I_{2}, I_{3}

and

I_{4}

are respectively the moments of inertia about axis

1, 2, 3

and

4

which are in the plane of the square plate. Then, the moment of inertia

I_{0}

of the plate about an axis passing through its centre

O

and perpendicular to the plane of the plate will be equal to : (Choose the correct option(s))

Join BYJU'S Learning Program

Let I1,I2 and I3 be the moment of inertia uniform plate about axes AOC,xDx′ and yBy′ respectively as shown in the figure. The moment of inertia of the plate I1:I2:I3 are in the ratio

The correct options are A 1:17:17 D 1:7:7 I1=ma212I2=I1+mr2=ma212+ma22=712ma2∴I1:I2=1:7

Let $I_{1}, I_{2}$ and $I_{3}$ be the moment of inertia uniform plate about axes $A O C, x D x^{'}$ and $y B y^{'}$ respectively as shown in the figure. The moment of inertia of the plate $I_{1} : I_{2} : I_{3}$ are in the ratio

The correct options are
A $1 : \frac{1}{7} : \frac{1}{7}$
D $1 : 7 : 7$
$I_{1} = \frac{m a^{2}}{12}$
$I_{2} = I_{1} + m r^{2}$
$= \frac{m a^{2}}{12} + \frac{m a^{2}}{2} = \frac{7}{12} m a^{2}$
$∴ I_{1} : I_{2} = 1 : 7$