The length of metallic wire is $\ell_{1}$ when tension in it is $T_{1}$. It is $\ell_{2}$ when the tension is $T_{2}$. The original length of the wire will be -
$\frac{\ell_{1}+\ell_{2}}{2}$
$\frac{\mathrm{T}_{2} \ell_{1}+\mathrm{T}_{1} \ell_{2}}{\mathrm{~T}_{1}+\mathrm{T}_{2}}$
$\frac{\mathrm{T}_{2} \ell_{1}-\mathrm{T}_{1} \ell_{2}}{\mathrm{~T}_{2}-\mathrm{T}_{1}}$
$\frac{\mathrm{T}_{1} \ell_{1}-\mathrm{T}_{2} \ell_{2}}{\mathrm{~T}_{2}-\mathrm{T}_{1}}$
Correct Option: , 3
Assuming Hooke's law to be valid.
$\mathrm{T} \propto(\Delta \ell)$
$\mathrm{T}=\mathrm{k}(\Delta \ell)$
Let, $\ell_{0}=$ natural length (original length)
$\Rightarrow \mathrm{T}=\mathrm{k}\left(\ell-\ell_{0}\right)$
so, $\mathrm{T}_{1}=\mathrm{k}\left(\ell_{1}-\ell_{0}\right) \& \mathrm{~T}_{2}=\mathrm{k}\left(\ell_{2}-\ell_{0}\right)$
$\Rightarrow \frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}=\frac{\ell_{1}-\ell_{0}}{\ell_{2}-\ell_{0}}$
$\Rightarrow \ell_{0}=\frac{\mathrm{T}_{2} \ell_{1}-\mathrm{T}_{1} \ell_{2}}{\mathrm{~T}_{2}-\mathrm{T}_{1}}$
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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,