Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa

A circular disc X of radius R is made from an iron  plate of thickness t  and another disc Y of radius 4R  is made from an iron plate of thickness t/4. Then the relation between the moment of inertia. I_{X} and I_{Y} is  

Option 1)

I_{Y}= 32I_{X}

 Option 2)

I_{Y}= 16I_{X}
Option 3)

I_{Y}= I_{X}

 Option 4)

I_{Y}= 64I_{X}

Answers (1)

best_answer

As we learnt in

Moment of inertia for disc -

I=\frac{1}{2} MR^{2}

 

- wherein

About an axis perpendicular to the plane of disc & passing through its centre .

 

 Mass of Disc X=\left ( \pi R^{2} t \sigma \right )\ \; \Rightarrow\ \; I_{X}=\frac{MR^{2}}{2}=\frac{\left ( \pi R^{2}t\sigma \right )R^{2}}{2}=\frac{\pi R^{2}\sigma t}{2}

Mass of Disc Y=I_{Y}=\frac{M\left ( {4R} \right )^{2}}{2}=\frac{\pi\left ( 4R \right )^{2}}{2}\frac{t}{4}\sigma 16R^{2}=32{\pi}R^{4}t \sigma

\frac{I_{X}}{I_{Y}}=\frac{\pi R^{4}\sigma t}{2}\times\frac{1}{32{\pi}R^{4}\sigma t}=\frac{1}{64}

I_{Y}=64 \; I_{X}

 


Option 1)

I_{Y}= 32I_{X}

This is an incorrect option.

Option 2)

I_{Y}= 16I_{X}

This is an incorrect option.

Option 3)

I_{Y}= I_{X}

This is an incorrect option.

Option 4)

I_{Y}= 64I_{X}

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 2024 Session 2: Last day to challenge answer key today
anam-khan

BTech admission 2024 without JEE; top government engineering colleges, upcoming entrance exams
anam-khan

JEE Main 2024 answer key out at jeemain.nta.ac.in; raise objections till April 14

Latest Question