SATHEE: Rotational Motion Question 140

Rotational Motion Question 140

Question: Consider a uniform square plate of side $a$ and mass $M$ . The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its comers is

Options:

A) $\frac{5}{6} M a^{2}$

B) $\frac{1}{12} M a^{2}$

C) $\frac{7}{12} M a^{2}$

D) $\frac{2}{3} M a^{2}$

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Answer:

Correct Answer: D

Solution:

[d] For a rectangular sheet moment of inertia passing through O, perpendicular to the plate is

$I_{O} = M (\frac{a^{2} + b^{2}}{12})$

For square plate it is $\frac{M a^{2}}{6}$ $(a s a = b)$

$r = \sqrt{\frac{a^{2}}{4} + \frac{a^{2}}{4}} = \frac{a}{\sqrt{2}}$

$∴ r^{2} = \frac{a^{2}}{2}$

$∴$ Moment of inertia about B parallel to the axis through O is

$I_{B} = I_{O} = M r^{2} = \frac{M a^{2}}{6} + \frac{M a^{2}}{2} = \frac{2 M a^{2}}{6}$ $I = \frac{2}{3} M a^{2}$

Rotational Motion Question 140

Question: Consider a uniform square plate of side $a$ and mass $M$ . The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its comers is

Options:

Answer:

Solution:

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Rotational Motion Question 140

Question: Consider a uniform square plate of side a and mass M . The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its comers is

Options:

Answer:

Solution:

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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Question: Consider a uniform square plate of side $a$ and mass $M$ . The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its comers is