Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Consider a uniform rod of mass and length l pivoted about its centre. A mass m moving with velocity <img alt="v" src="http://entrancecorner.oncodecogs.com/gif.latex

Consider a uniform rod of massM=4m and length l pivoted about its centre. A mass m moving with velocity v making angle \theta =\frac{\pi }{4} to the rod's long axis collides with one end of the rod and sticks to it. The angular speed of the rod - mass system just after the collision is :   
Option: 1 \frac{4}{7}\frac{v}{l}

Option: 2 \frac{3\sqrt{2}}{7}\frac{v}{l}

Option: 3 \frac{3}{7\sqrt{2}}\frac{v}{l}  

Option: 4 \frac{3}{7}\frac{v}{l}

Answers (1)

best_answer

 

Let us conserve angular momentum about O:-

           So, L_i=\left ( \frac{mv}{\sqrt2} \right )\times \frac{l}{2}, where \left ( \frac{mv}{\sqrt2} \right ) is linear momentum and \left ( \frac{l}{2} \right ) is the distance from centre O.

Now, L_f=I\omega

Here, I=\frac{4ml^2}{12}+{m\left (\frac{l}{2} \right )^2}=\frac{7ml^2}{12}

So, L_i=L_f\Rightarrow \omega=\frac{6v}{7\sqrt2 l}= \frac{3\sqrt2v}{7 l}

So the correct graph is given in option 2.

Posted by

vishal kumar

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 Registration Live: NTA session 1 application last date today; official website, syllabus
anam-khan

JEE Main 2025 session 1 registration ends today at jeemain.nta.nic.in; application correction from November 26
anam-khan

JEE Main 2025 registration ends tomorrow; changes introduced in exam this year

Latest Question