Initial angular velocity of a circular disc of mass  M  is  \omega _{1}  . Then two small spheres of mass  m are attached gently to two diametrically opposite points on the edge of the disc What is the final angular velocity of the disc ?

Option 1)

\left ( \frac{M+m}{M} \right )\omega _{1}

Option 2)

\left ( \frac{M+m}{m} \right )\omega _{1}

Option 3)

\left ( \frac{M}{M+4m} \right )\omega _{1}

Option 4)

\left ( \frac{M}{M+2m} \right )\omega _{1}

Answers (1)

As we learn in

Law of conservation of angular moment -

\vec{\tau }= \frac{\vec{dL}}

- wherein

If net torque is zero

i.e. \frac{\vec{dL}}= 0

\vec{L}= constant

angular momentum is conserved only when external torque is zero .

 

 L_{1}=L_{2}\; \Rightarrow I_{1}\omega {}_{1}=I_{2}\omega {}_{2}

I_{1}=\frac{1}{3}mR^{2}

I_{2}=\frac{1}{2}mR^{2}+2mR^{2}

\frac{1}{2}mR^{2}\omega_{1}=\frac{MR^{2}+4mR^{2}}{2} \;\omega {}_{2}

\omega{}_{2}=\frac{M\omega{}_{1}}{M+4m}

 


Option 1)

\left ( \frac{M+m}{M} \right )\omega _{1}

This is an incorrect option.

Option 2)

\left ( \frac{M+m}{m} \right )\omega _{1}

This is an incorrect option.

Option 3)

\left ( \frac{M}{M+4m} \right )\omega _{1}

This is the correct option.

Option 4)

\left ( \frac{M}{M+2m} \right )\omega _{1}

This is an incorrect option.

Most Viewed Questions

Preparation Products

Knockout JEE Main April 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
Buy Now
Knockout JEE Main May 2021

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 22999/- ₹ 9999/-
Buy Now
Test Series JEE Main May 2021

Unlimited Chapter Wise Tests, Unlimited Subject Wise Tests, Unlimited Full Mock Tests, Get Personalized Performance Analysis Report,.

₹ 6999/- ₹ 2999/-
Buy Now
Knockout JEE Main May 2022

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 34999/- ₹ 14999/-
Buy Now
JEE Main Rank Booster 2021

Booster and Kadha Video Lectures, Unlimited Full Mock Test, Adaptive Time Table, 24x7 Doubt Chat Support,.

₹ 13999/- ₹ 6999/-
Buy Now
Boost your Preparation for JEE Main 2021 with Personlized Coaching
 
Exams
Articles
Questions