A light rod of length l has two masses m1 and m2 attached to its two ends. The moment of inertia of the system about an axis perpendicular  to the rod and passing through the center of mass is

  • Option 1)

    \frac{{m_1 m_2 }}{{m_1 + m_2 }}l^2

  • Option 2)

    \frac{{m_1 + m_2 }}{{m_1 m_2 }}l^2

  • Option 3)

    \left( {m_1 + m_2 } \right)l^2

  • Option 4)

    \sqrt {m_1 + m_2 } l^2

 

Answers (1)

As we learnt in

Moment of inertia for system of particle -

I= m_{1}r_{1}^{2}+m_{2}r_{2}^{2}+.........m_{n}r_{n}^{2}

dpi{100} = sum_{i=1}^{n}: m_{i}r_{i}^{2}

 

- wherein

Applied when masses are placed discretely.

 

I=m_{1}r_{1}^{2}+m_{2}r_{2}^{2}

=m_{1}\left(\frac{m_{2}}{m_{1}+m_{2}}l \right )^{2}+m_{2}\left(\frac{m_{2}}{m_{1}+m_{2}}l \right )^{2}

=\frac{m_{1}m_{2}(m_{1}+m_{2})l^{2}}{(m_{1}+m_{2})^{2}}

=\frac{m_{1}m_{2}l^{2}}{(m_{1}+m_{2})}


Option 1)

\frac{{m_1 m_2 }}{{m_1 + m_2 }}l^2

Correct

Option 2)

\frac{{m_1 + m_2 }}{{m_1 m_2 }}l^2

Incorrect

Option 3)

\left( {m_1 + m_2 } \right)l^2

Incorrect

Option 4)

\sqrt {m_1 + m_2 } l^2

Incorrect

Most Viewed Questions

Preparation Products

Knockout NEET Aug 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 NEET Aug 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 NEET Aug 2021

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

₹ 6999/- ₹ 2999/-
Buy Now
Rank Booster NEET 2021

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

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