Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • A rod of mass  M, length  l  and cross sectional area  A, made of material of young's modulus  Y  is rotated about its one end in horizontal plane with c

A rod of mass  M, length  l  and cross sectional area  A, made of material of young's modulus  Y  is rotated about its one end in horizontal plane with constant angular speed \omega.
It's extension is 

Option: 1

\frac{M \omega^2 l^2}{3 A Y}


Option: 2

\frac{M \omega^2 l^2}{ A Y}


Option: 3

\frac{M \omega^2 l^3}{A Y}


Option: 4

\frac{M \omega^2 l^2}{4 A Y}


Answers (1)

best_answer

For the element of mass dM


-(d F) =(d M) \omega^2 x \\
F =-\int_l^x\left(\frac{M}{l} d x\right) \omega^2 x \\
F =\frac{M}{2 l} \omega^2 (l^2-x^2)

Now, using d l =\frac{F(d x)}{A Y}

d l =\frac{M \omega^2}{2 l} \,\,\,\,\frac{\left(l^2-x^2\right)}{A Y} d x \\
\Delta l =\frac{M \omega^2}{2YA l} \int_0^l\left(l^2-x^2\right) d x \\

\Delta l =\frac{M \omega^2 l^2}{3 A Y}

Posted by

Pankaj

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

JAC Chandigarh Counselling 2025: Round 1 seat allotment result out for BTech admissions
anam-khan

JoSAA round 5 seat allotment result 2025 out on josaa.nic.in
anam-khan

BTech aspirant from north-east or UT? Apply for CSAB NEUT counselling 2025 today

Latest Question