Get Answers to all your Questions

header-bg qa

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)

best_answer

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

Posted by

Plabita

View full answer

NEET 2024 Most scoring concepts

    Just Study 32% of the NEET syllabus and Score up to 100% marks