Question:
A uniform thin bar of mass $6 \mathrm{~kg}$ and length $2.4$ meter is bent to make an equilateral hexagon. The moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of hexagon is _____________ $\times 10^{-1} \mathrm{~kg} \mathrm{~m}^{2}$.
Solution:
$61=2.4 \ell=0.4 \mathrm{~m}$
$\sin 60^{\circ}=\frac{r}{\ell}$
$r=1 \sin 60^{\circ}=\frac{\ell \sqrt{3}}{2}$
MOI, $\quad \mathrm{I}=\left[\frac{\mathrm{m} \ell^{2}}{12}+\mathrm{mr}^{2}\right] 6$
$=\left[\frac{\mathrm{m} \ell^{2}}{12}+\mathrm{m}\left(\frac{\ell \sqrt{3}}{2}\right)^{2}\right] 6$
$=5 \mathrm{ml}]^{2}$
$=5 \times 1 \times 0.16$
$=0.8$
$\mathrm{I}=8 \times 10^{-1} \mathrm{~kg} \mathrm{~m}^{2}$
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,
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