Given below are two statements : one is labelled as Assertion $\mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$. Assertion A : Moment of inertia of a circular disc of mass ' $M$ ' and radius ' $R$ ' about $X, Y$ axes (passing through its plane) and Z-axis which is perpendicular to its plane were found to be $I_{x}, I_{y}$ and $I_{z}$ respectively. The respective radii of gyration about all the three axes will be the same.
Reason $\mathbf{R}$ : A rigid body making rotational motion has fixed mass and shape. In the light of the above statements, choose the most appropriate answer from the options given below :
Both $\mathbf{A}$ and $\mathbf{R}$ are correct but $\mathbf{R}$ is NOT the correct explanation of $\mathbf{A}$.
$\mathbf{A}$ is not correct but $\mathbf{R}$ is correct.
$\mathbf{A}$ is correct but $\mathbf{R}$ is not correct.
Both $\mathbf{A}$ and $\mathbf{R}$ are correct and $\mathbf{R}$ is the correct explanation of $\mathbf{A}$.
Correct Option: , 2
$\mathrm{I}_{\mathrm{z}}=\mathrm{I}_{\mathrm{x}}+\mathrm{I}_{\mathrm{y}}$ (using perpendicular axis theorem)
$\& \mathrm{I}=\mathrm{mk}^{2}(\mathrm{~K}$ : radius of gyration $)$
so $\mathrm{mK}_{\mathrm{z}}^{2}=\mathrm{mK}_{\mathrm{x}}^{2}+\mathrm{mK}_{\mathrm{y}}^{2}$
$\mathrm{K}_{\mathrm{z}}^{2}=\mathrm{K}_{\mathrm{x}}^{2}+\mathrm{K}_{\mathrm{y}}^{2}$
so radius of gyration about axes $\mathrm{x}, \mathrm{y} \& \mathrm{z}$ won't be same hense asseration $A$ is not correct reason $R$ is correct statement (property of a rigid body)
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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,