A small block of superdense material has a mass of $3 \times 10^{24} \mathrm{~kg}$. It is situated at a height $h$ (much smaller than the earth's surface) from where it falls on the earth's surface. Find its speed when its height from the earth's surface has reduced to $\mathrm{h} / 2$. The mass of the earth is $3 \times 10^{24} \mathrm{~kg}$.
b-block
e-earth
Use C.O.L.M
$M_{e} V_{e}=m_{b} V_{b}$
$M_{e} V_{e}=m_{b} V_{b}$
$V_{e}=\frac{m_{b} V_{B}}{M}$
Use C.O.E.L
$G M_{e} m_{b}\left[\frac{1}{R+\left(\frac{h}{2}\right)}-\frac{1}{R+h}\right]=\frac{1}{2} M_{e} V_{e}^{2}+\frac{1}{2} m_{b} V_{b}^{2}$
$\Rightarrow G M_{e} m_{b}\left[\frac{2}{2 R+h}-\frac{1}{R+h}\right]=\frac{1}{2} M_{e} \frac{m_{b}^{2} V_{b}^{2}}{M_{e}^{2}}+\frac{1}{2} m_{b} V_{b}^{2}$
$=\frac{1}{2} m_{b} V_{b}^{2}\left(\frac{m_{b}}{M_{e}}+1\right)$
$\Rightarrow G M_{e}\left[\frac{h}{2 R^{2}+3 R h+h^{2}}\right]=\frac{1}{2} V_{b}^{2}\left(\frac{3}{2}\right)$
$\mathrm{h}<<\mathrm{R}$
$\Rightarrow \frac{G M_{e} h}{2 R^{2}}=\frac{1}{2} V_{b}^{2}\left(\frac{3}{2}\right) \Rightarrow V_{B}=\sqrt{\frac{2 g h}{3}}$
- 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,
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,