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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}

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

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

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1 : 7 : 7

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Solution

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

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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

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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))

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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 $1 : 7 : 7$
$I_{1} = \frac{m a^{2}}{12}$
$I_{2} = I_{1} + m r^{2}$
$= \frac{m a^{2}}{12} + \frac{m a^{2}}{2} = \frac{7}{12} m a^{2}$
$∴ I_{1} : I_{2} = 1 : 7$