Advertisements
Advertisements
Question
Four particles, each of mass M and equidistant from each other, move along a circle of radius R under the action of their mutual gravitational attraction. Calculate the speed of each particle.
Advertisements
Solution
Force acting on a particle
= `"GM"^2/(2"R")^2 + "GM"^2/(("R"/sqrt2)^2) cos 45° + "GM"^2/(("R"/sqrt2)^2) cos 45°`
E = `"GM"^2/"R"^2 [1/4 + 1/sqrt2]`
Since particle, moving circular path experience centripetal force,
E = `"MV"^2/"R"`
`"MV"^2/"R" = "GM"^2/"R"^2 [1/4 + 1/sqrt2]`
∴ V = `1/2 sqrt("GM"/"R" (1 + 2sqrt2))`
APPEARS IN
RELATED QUESTIONS
The kinetic energy of the satellite orbiting around the Earth is __________.
What are geostationary and polar satellites?
Define weight
Why is there no lunar eclipse and solar eclipse every month?
How will you prove that Earth itself is spinning?
Explain in detail the idea of weightlessness using the lift as an example.
Derive an expression for escape speed.
Derive the time period of the satellite orbiting the Earth.
Derive an expression for the energy of satellite.
Explain in detail the geostationary and polar satellites.
