Two small bodies of masses $10 \mathrm{~kg}$ and $20 \mathrm{~kg}$ are kept a distance $1.0 \mathrm{~m}$ apart and released, Assuming that only mutual gravitational forces are acting; find the speeds of the particles when the separation decreases to $0.5 \mathrm{~m}$.
$m_{1}=10 \mathrm{~kg}, \quad m_{2}=20 \mathrm{~kg}$
Initially,
Finally,
$\underset{\gamma_{f}=0.5 \mathrm{~m}}{\stackrel{10 \mathrm{~kg}}{\rightarrow} \mathrm{O}_{1} \quad V_{2} \text { - 20kf }}$
If both bodies are taken as system.
$\vec{F}_{\text {ext }}=0$
$\vec{P}_{i}=\vec{P}_{f}$
$0+0=10 V_{1}-20 V_{2}$
$10 V_{1}=20 V_{2}$
$V_{1}=2 V_{2}$
Now, applying law of conservation of energy,
$T E_{i}=T E_{f}$
$\frac{-G m_{1} m_{2}}{r_{i}}+0+0=\frac{-G m_{1} m_{2}}{r_{f}}+\frac{1}{2} m_{1} v_{1}^{2}+\frac{1}{2} m_{2} v_{2}^{2}$
$\frac{-6.67 \times 10^{-11} \times 10 \times 20}{1}$
On solving,
$V_{1}=4.2 \times 10^{-5} \mathrm{~m} / \mathrm{s}$
and
$V_{2}=\frac{V_{1}}{2}=2.1 \times 10^{-5} \mathrm{~m} / \mathrm{s}$
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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,