A body of mass $m$ makes an elastic collision with another identical body at rest. Show that if the collision is not head-on, the bodies go right angle to each other after the collision.
If $m$ is not colliding head-on, along $x$-axis, use C.O.L.M $m v \cos \theta=m\left(v_{1} \cos \alpha+v_{2} \cos \beta\right)-(1)$
Along y-axis, $-m v \sin \theta=m\left(v_{1} \sin \alpha-v_{2} \sin \beta\right)-(2)$
Use C.O.E.L
$\frac{1}{2} m v^{2}=\frac{1}{2} m\left(v_{1}^{2}+v_{2}^{2}\right)$
Squaring (1) and (2) and add them,
$v^{2}=v_{1}^{2}\left(\cos ^{2} \alpha+\sin ^{2} \alpha\right)+v_{2}^{2}\left(\cos ^{2} \beta+\sin ^{2} \beta\right)+2 v_{1} v_{2}(\cos \alpha \cos \beta-\sin \alpha \sin \beta)$
$v^{2}=v_{1}^{2}+v_{2}^{2}+2 v_{1} v_{2} \cos (\alpha+\beta)$
$\cos (\alpha+\beta)=0=\pi / 2$
$\therefore \alpha+\beta=\pi / 2$
- JEE Main
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- Physics
- Kinematics 1D
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- Work, Power, Energy
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- Calorimetry
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- Thermal Expansion
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- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
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- Electrostatics
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- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
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- Error in Measurement & instruments
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- Electromagnetic Waves
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- 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,
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,