SATHEE: Rotation 1 Question 18

Rotation 1 Question 18

21. The moment of inertia of a thin square plate $A B C D$ , of uniform thickness about an axis passing through the centre $O$ and perpendicular to the plane of the plate is

$(1992, 2 M)$

(a) $I_{1} + I_{2}$

(b) $I_{3} + I_{4}$

(d) $I_{1} + I_{2} + I_{3} + I_{4}$

where, $I_{1}, I_{2}, I_{3}$ and $I_{4}$ are respectively moments of inertia about axes 1, 2, 3 and 4 which are in the plane of the plate.

Integer Answer Type Questions

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Answer:

Correct Answer: 21. (a, b, c)

Solution:

Since, it is a square lamina

$\begin{aligned} I_{3} = I_{4} \\ and I_{1} = I_{2} \end{aligned}$

(by symmetry)

From perpendicular axes theorem,

Moment of inertia about an axis perpendicular to square plate and passing from $O$ is

$I_{o} = I_{1} + I_{2} = I_{3} + I_{4}$

$Hence, I_{2} = I_{3}$

Rather we can say $I_{1} = I_{2} = I_{3} = I_{4}$

Therefore, $I_{o}$ can be obtained by adding any two i.e.

$\begin{aligned} I_{o} & = I_{1} + I_{2} = I_{1} + I_{3} \\ = I_{1} + I_{4} = I_{2} + I_{3} \\ = I_{2} + I_{4} = I_{3} + I_{4} \end{aligned}$

Rotation 1 Question 18

21. The moment of inertia of a thin square plate $A B C D$ , of uniform thickness about an axis passing through the centre $O$ and perpendicular to the plane of the plate is

Integer Answer Type Questions

Answer:

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Rotation 1 Question 18

21. 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

Integer Answer Type Questions

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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21. The moment of inertia of a thin square plate $A B C D$ , of uniform thickness about an axis passing through the centre $O$ and perpendicular to the plane of the plate is