Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

For the given uniform square lamina ABCD, whose centre is O ,

Option 1)
$I_{AC}=\sqrt{2}I_{EF}$
Option 2)
$\sqrt{2}I_{AC}=I_{EF}$

Option 3)
$I_{AD}=3I_{EF}$
Option 4)
$I_{AC}=I_{EF}$

Answers (1)

best_answer

As we learnt in

Perpendicular Axis theorem -

$I_{z}= I_{x}+I_{y}$

(for a body in XY plane )

- wherein

$I_{z}$ = moment of inertia about z axis

$I_{x}$ . $I_{y}$ : the moment of inertia about x & y axis in the plane of the body respectively.

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

a=b

$I_{EF}=M\frac{\left ( a^{2}+a^{2} \right )}{12}=\frac{Ma^{2}}{6}$

$I_{Z}=\frac{Ma^{2}}{6}+\frac{Ma^{2}}{6}=\frac{Ma^{2}}{6}$

By a theorem of the perpendicular axis.

$I_{AC}+I_{BD}=I_{Z}=I_{AC}=\frac{I_{2}}{2}=\frac{Ma^{2}}{6}$

Similarly

$I_{EF}=\frac{I_{Z}}{2}=\frac{Ma^{2}}{6}$

$\therefore\ \; I_{AC}=I_{EF}$

Option 1)

$I_{AC}= \sqrt{2}I_{EF}$

This is an incorrect option.

Option 2)

$\sqrt{2}I_{AC}= I_{EF}$

This is an incorrect option.

Option 3)

$I_{AD}= 3I_{EF}$

This is an incorrect option.

Option 4)

$I_{AC}= I_{EF}$

This is the correct option.

Posted by

perimeter

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2025: Hardwired to excel? Know BTech electrical engineering cut-offs at NITs

anam-khan

JEE Main 2025 chemistry needs conceptual understanding; 5 tips to score high

anam-khan

JEE Main 2025 exam city intimation slip for session 1 soon; paper pattern, exams from January 22

Latest Question