2 5. The gravitational field inside a spherical planet of uniform density, mass M, and radius...
Assume that a Spherical Planet Of Radius R, Has a Uniform Mass Density (Per Unit Volume) Distribution Throughout, Of Value Po. Also, Assume that There Is a Massive Dust Cloud In the Rest Of the Universe, Which Decays Exponentially In Radius, r, Away From the Surface Of the Planet, Where the Mass Density Varies As ρ(r) = Po exp| | | |, For r2R- a) Using the Integral Form Of Gauss's 6. Law, [n.gda--4πGJsoh', And Spherical Coordinates (Specifically Using the...
Assume that a Spherical Planet Of Radius R, Has a Uniform Mass Density (Per Unit Volume) Distribution Throughout, Of Value Po. Also, Assume that There Is a Massive Dust Cloud In the Rest Of the Universe, Which Decays Exponentially In Radius, r, Away From the Surface Of the Planet, Where the Mass Density Varies As ρ(r) = Po exp| | | |, For r2R- a) Using the Integral Form Of Gauss's 6. Law, [n.gda--4πGJsoh', And Spherical Coordinates (Specifically Using the...
A satellite of mass m is in a circular orbit of radius R2 around a spherical planet of radius R1 made of a material with density ρ. ( R2 is measured from the center of the planet, not its surface.) Use G for the universal gravitational constant.A) Find the kinetic energy of this satellite, KExpress the satellite's kinetic energy in terms of G, m, π, R1, R2, and ρ.B) Find U, the gravitational potential energy of the satellite. Take the gravitational potential...
2. Assume the earth is a uniform sphere of mass M and radius R. (Its mass-density ρ--M/V is therefore constant.) a) Find the force of gravity exerted on a point mass m located inside the earth, as a function of its distance from the earth's centre. (You may make use of results derived in class for a thin spherical shell.) b) Find the difference in the gravitational potential energy of the mass, between the centre of the earth and the...
A metal ring of radius a and mass m falls into a constant and uniform gravitational field, with the acceleration g, inside a magnetic field, in which the vertical component Bz depends on z. The plane of the ring remains horizontal and the resistance of the ring is R. If the inductance of the ring is negligible, prove that for a long fall, the ring's velocity becomes independent of z if (dBz/dz) → b1 for large |z|, where b1 is...
3 GM2 (5) The gravitational potential of a uniform-density sphere of mass M and radius R is E,-- Consider a white dwarf star which contains N electrons whose Fermi energy is Es. Since kaT <<Ef, the average electron energy is 3/5Er (derived in assignment 1) and the total electron energy is Ed-3/5NEs. The energies of the nuclei can be neglected. OE (a) Derive an expression for the gravitational pressure: P- OE (b) Derive an expression for the degeneracy pressure: Pa-...
1a) What is the gravitational field strength on the planet Jupiter? Given it's mass is 1.90 x 1027 kg and it's equatorial radius is 7.15x107 m. 1b) What is the gravitational field strength on the planet Mercury? Given it's mass is 3.30 x 1023 kg and it's equatorial radius is 2.44x106 m.
(c) (i) On the surface of a planet of mass \(\mathrm{M}\) and radius \(\mathrm{R}\), the gravitational potential energy of a molecule of mass \(\mathrm{m}\) is \(-\frac{G M m}{R}\). Show that the escape speed of a molecule from the surface is \(\sqrt{\frac{2 G M}{R}}\).(ii) The rms thermal speed of a molecule of mass \(m\) is given by \(v_{\text {th }}=\left(\frac{3 k T}{m}\right)^{1 / 2}\) where \(k\) is Boltzmann's constant . Using the appropriate temperature value from part (b) calculate the \(\mathrm{rms}\)...
8. The magnitude of the gravitational field on the surface of a particular planet is 2g. The planet's mass is half the mass of Earth. What is the planet's radius in terms of the radius R of Earth? (B) RE/2 (C) Rel (D) 2RE
An insulating spherical shell of inner radius a 0.100 m and outer radius b 0.200 m has a non uniform charge density given by ρ(r)-α/r, where α +7.00 x 10-10 C/m4 (a) What is the electric field at a distance of 0.050 m from the center of the spherical shell? (b) What is the electric field at a distance of 0.150 m from the center of the spherical shell? (c) If an electron is orbiting the spherical shell at a...