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(II) Suppose the mass of the Earth were doubled, but itkept the same density and spherical shape. How would theweight of objects at the Earth's surface change?

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multiplied by $2^{1 / 3}$

Physics 101 Mechanics

Chapter 6

Gravitation and Newton's Synthesis

Physics Basics

Newton's Laws of Motion

Applying Newton's Laws

Gravitation

Cornell University

University of Washington

Simon Fraser University

Lectures

03:43

In physics, dynamics is the branch of physics concerned with the study of forces and their effect on matter, commonly in the context of motion. In everyday usage, "dynamics" usually refers to a set of laws that describe the motion of bodies under the action of a system of forces. The motion of a body is described by its position and its velocity as the time value varies. The science of dynamics can be subdivided into, Dynamics of a rigid body, which deals with the motion of a rigid body in the frame of reference where it is considered to be a rigid body. Dynamics of a continuum, which deals with the motion of a continuous system, in the frame of reference where the system is considered to be a continuum.

03:55

In physics, orbital motion is the motion of an object around another object, which is often a star or planet. Orbital motion is affected by the gravity of the central object, as well as by the resistance of deep space (which is negligible at the distances of most orbits in the Solar System).

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6.13. We suppose that the mass of the earth is doubled, but the same density, its density remains the same and that it's still spherical, of course, and we want to know how the weight of objects the Earth's surface would change. So first we should find the, um, acceleration due to gravity in terms of the density of the Earth. So this is the acceleration due to gravity of the surface of the earth. Now we know that the density is going to just be It's mass divided by its volume, which is 4/3. I are huge so that in terms of its density, the radius of the earth is three times it's asked, divided by four pi times its density to the 1/3 power so we can call the original RG not or whatever. Um, I was going to be the gravitational, constant times, the mass of the earth divided by this squared. So we have three e or over for hi Rho to the 2/3. So simplifying this little bit we get gravitational constant is still there. We have the mass of the earth to the 1/3 power divided by three over four pi and throw the density to the 2/3. So now we have an expression for G just in terms of the Earth's mass and its density. We're told the density is staying the same. So our new G, we double the mass, the density stays the same. So we see that this is going to be everything here. Except for this too. Under the 1/3 power is exactly the same as it was over here. So we have the third route of two times G. So this is the factor by which the weight of everything would change.

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