The gravitational force exerted by the planet Earth on a unit mass at a distancer from the center of the planet is GMr if rR where M is the mass of Earth, Ris its radius, and G is the gravitational constant. Is F a continuous function of r?

The gravitational force exerted by the planet Earth on a unit mass at a distancer from the center of the planet is GMr if rR where M is the mass of Earth, Ris its radius, and G is the gravitational constant. Is F a continuous function of r?

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter6: Applications Of Newton's Laws

Section: Chapter Questions

Problem 129CP: In a later chapter, you will find that the weight of a particle varies with altitude such that...

See similar textbooks

Related questions

Q: A spherical planet has an outer radius R; its density p varies as a function of distance r given by…

A: Given data: The density function is, ρr=3-2r2R2.

Q: 2.) A = 8i + 4j – 2k lb B = 2j + 6k ft C = 3i – 2j + 4k ft a.) Å · B b.) Ảx C c.) Find the angle…

A: GivenA = 8i + 4j — 2k lbB = 2j + 6k ftC = 3i — 2j + 4k ft

Q: An object is released from rest when it is a height h above the surface of a planet of mass M and…

Q: Consider a moon orbiting planet A in a radius R with a given period T. If the planet has a mass of…

Q: Assume that planet A has radius RA and mass MA, and planet B has radius Rg and mass Mg. Let gA and…

A: radius of planet A=RAmass of planet A=MAradius of planet B=RBmass of planet B=MB

Q: Determine the simplified ratio of the velocities of a low earth satellite travelling 300 km above…

Q: A hypothetical planet has a radius 1.1 times that of Earth, but has the same mass. What is the…

A: Given: The radius of the planet is 1.1 times radius of the earth. The mass of the planet is same as…

Q: A mass M is split into two parts, m and M - m, which are then separated by a certain distance. What…

A: Write the expression for gravitational force. Use m and M – m for masses in the above expression.

Q: A satellite of Mars, called Phobos, has an orbital radius of 9.4 x 10° m and a period of 2.8 x 10“…

A: The satellite has an orbital radius of, r= 9.4 × 106 m and a period of T=2.8 x 104 s. It is required…

Q: The potential function for the gravitational force field due to a mass M at the origin acting on a…

Q: the mass or the carth is Me, show thnat the gravitational potential energy of a body of mass m…

Q: Obtain the required relation please

A: Using the concept of relative velocity in x-axis;

Q: A nonuniform thin rod of length L lies on the x axis. One end of the rod is at the origin, and the…

A: (a) Total mass of the rod

Q: At what altitude h above the north pole is the weight of an object reduced to 27% of its…

Q: Given a force F that has magnitude of 240 N, find the angles ex, Oy, 0z that define the direction of…

Q: A star is pulsating isotropic ally. Its gravitational fore on any body, at distances much larger…

A: ans ;- option (a)

Q: The gravitational field a distance r inside a spherical cloud of radius R and total mass M is given…

A: Given, Gravitational field, g=-GNMR4r2

Q: The radius of Earth is about 6400 km. How far upward from the surface would a body feel a value of g…

A: Acceleration due to gravity at h height g' = GM/(R+h)2 where G = universal gravitational constant…

Q: Consider a uniform gravitational field (a fair approximation near the surface of a planet). Find

Q: Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets…

A: Given : Mass of Venus, MV = 0.815 ME Mass of Jupiter, MJ = 318 ME Mass of Saturn,…

Q: In Pole to Pole, an early science fiction story by George Griffith, three explorers attempt to…

Q: Consider a pulsar, a collapsed star of extremely high density, with a mass M equal to that of the…

Q: An exoplanet (JB-2285), located in the galaxy closest to ours, uses a system where the units of mass…

A: Given: unit of mass = phljmthunit of force = xwyflrg'=710g = 0.7*9.8066g'=6.865 m/s2 also, 1xwyflr =…

Q: It is found that when a particular object with a mass of 0.41 kg is released from rest while…

A: Given data: Mass of the object, m = 0.41 kg, Coefficient of proportionality in the resistive force,…

Q: In Pole to Pole, an early science fiction story by George Griffith, three explorers attempt to…

A: Mass of earth= 5.972 x 10 24 Kilogram Radius of Earth= 6380 x 103m Value of Gravitational Constant,…

Q: The weight of bodies my change somewhat from one location to another as a result of the variation of…

A: The gravitational acceleration as a function of elevation z is Where,

Q: Assume the earth is a uniform sphere of mass M and radius R. As strange as it may sound, if one can…

Q: A uniform solid sphere of radius R produces a gravitational acceleration of ag on its surface. At…

A: Given: A uniform solid sphere of radius R produces a gravitational acceleration of ag on its…

Q: How much work is required to lift a 500-kg satellite to an altitude of 1 · 10° m above the surface…

A: Given values- Mass of satellite =m=500 kgAltitude=h=1×106 m Gravitational…

Q: Assume that planet A has radius RA and mass MA, and planet B has radius Rg and mass Mg. Let ga and…

A: Given data: - The radius of the planet B is RB. The mass of the planet A is MA. The radius of the…

Q: At what altitude h above the north pole is the weight of an object reduced to one-half of its earth-…

Q: 16-9. Show that the escape velocity from a planet's surface is given by v = (2gR)/2 where g is the…

Q: Assuming that the Earth has a uniform density, ρ=5540.0⁢ kg/m3, what is the value of the…

Q: Let ΔgM represent the difference in the gravitational fields produced by the Moon at the points on…

Q: A uniform, solid sphere, of radius R=0.84km, produces a gravitational acceleration of ag on its…

A: Given,

Q: Assume that planet A has radius RA and mass MA, and planet B has radius Rg and mass Mg. Let ga and…

A: Given: MA=MBRA=2RBIn this question we have to find gAgB

Q: Assume a planet is a uniform sphere of radius R that (somehow) has a narrow radial tunnel through…

A: I this question we have to assume a planet is a uniform sphere of radius R that (somehow) has a…

Q: •6 G0 In Fig. 13-32, a square of edge length m 20.0 cm is formed by four spheres of masses m¡ = 5.00…

A: Given: m1=5g=5×10-3kgm2=3g=3×10-3kgm3=1g=1×10-3kgm4=5g=5×10-3kgm5=2.5g=2.50×10-3kg l=20 cm

Q: A space shuttle which moves in a circular orbit around the earth at a height h 150 mi above its…

A: Given : height of the shuttle from the surface of the earth, h=150 mi speed of the shuttle at this…

Q: Consider a satellite in elliptical orbit around a planet of mass M, and suppose that physical units…

Q: The density of a sphere is giving by p(r)=C/r. The sphere has a radius of 5.0 m and a mass of…

A: Radius of the sphere r =5 m Mass of the sphere m =1×1011 kg The density of the sphere ρ(r)=C/r

Q: The gravitational force exerted by the earth on a unit massat a distance r from the center of the…

A: A function is continuous if limx→a-f(x)=limx→a+f(x)=f(a) Simply in words left-hand side =right- hand…

Q: Two points are given in polar coordinates by (r, θ) = (1.80 m, 50.0°) and (r, θ) = (4.00 m,…

Question

The gravitational force exerted by the planet Earth on a unit
mass at a distancer from the center of the planet is
GMr
if r<R
R
F(r)
GM
if r>R
where M is the mass of Earth, Ris its radius, and G is the
gravitational constant. Is F a continuous function of r?

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Show that the areal velocity for a circular orbit of radius r about a mass M is At=12GMr . Does your expression give the correct value for Earth’s areal vilocity about the Sun?
In a later chapter, you will find that the weight of a particle varies with altitude such that w=mgr02r2where r0is the radius of Earth and ris the distance from Earth’s center. If the particle is fired vertically with velocity v0from Earth’s surface, determine its velocity as a function of position r. (Hint: use adr=vdv, the rearrangement mentioned in the text.)
Compute directly the gravitational force on a unit mass at a point exterior to a homogeneous sphere of matter.
Check Your Understanding Consider the density required to make Earth a black hole compared to that required for the Sun. What conclusion can you draw from this comparison abut what would be required to create a black hole? Would you expect the Universe to have many black holes with small mass?
On a planet whose radius is 1.2107m , the acceleration due to gravity is 18m/s2 . What is the mass of the planet?
The gravitational force exerted by the earth on a unit massat a distance r from the center of the planet is where M is the mass of the earth,R is its radius, and G isthe gravitational constant. Is F a continuous function of r ?
A solid copper sphere of mass M and radius R has a cavity of radius ½ R. Inside the cavity a particle of mass m placed a distance d > R from the center of the sphere along the line connecting the centers of the sphere and the cavity. Find the gravitational force on m.
97 PROBLEMS 2-45. Describe how to determine whe ther an equilibrium is stable or unstable when (dUdx),0. 2-46. Write the criteria for determining whether an equilibrium is stable or unstable when all derivatives up through order n, (d" U/ dx ") 0. 247. Consider a particle moving in the rCrion
the mass or the carth is Me, show thnat the gravitational potential energy of a body of mass m located a distance r from the center of the earth is V, = -GM¸m/r. Recall that the gravitational force acting between the earth and the body is F = G(M¸m/P), Eq. 13-1. For the calculation, locate the datum at r→ ∞. Also, prove that F is a conservative force.
The radius Rhand mass Mh of a black hole are related by Rh = 2GMh/c2, where c is the speed of light. Assume that the gravitational acceleration agof an object at a distance ro= 1.001Rh from the center of a black hole is given by ag = G M / r2 (it is, for large black holes).(a) In terms of Mh, find ag at ro.(c) What is ag at rofor a very large black hole whose mass is 1.69 × 1015 times the solar mass of 1.99 × 1030 kg?(d) If an astronaut with a height of 1.73 m is at rowith her feet toward this black hole, what is the difference in gravitational acceleration between her head and her feet ahead-afeet?
A mood of a mass m and raduis a is orbiting a planet of mass M and if radius b at a distance d (center to center) in a circular orbit. Derive an expression for the speed of the mood v in terms of M,d and the gravitational constant G.
A tunnel is drilled from the surface of a planet straight down to its antipodal pointon the other side of the planet. A particle at the surface is dropped from rest intothe tunnel. Denote the position of the particle from the planet’s center at time t byr(t). Assume that the gravitational force the particle experiences is due only to themass of the planet within the sphere of radius r(t). Calculate the time (in seconds)the particle will take to reach the other end of the planet. Let the radius of the entireplanet be R = 20 × 106 m and take 4.9 as the value of g