Suppose a large spherical object, such as a planet, with radius R and mass M has a narrow tunnel passing diametrically through it. A particle of mass m is inside the tunnel at a distance x less than or equal to R from the center. It can be shown that the net gravitational force on the particlei s due entirely to the sphere of mass with radius r ≤ ;x there is no net gravitational force from the mass in the spherical shell with r > .x a. Find an expression for the gravitational force on the particle, assuming the object has uniform density. Your expression will be in terms of ,x R, m, M, and any necessary constants. b. You should have found that the gravitational force is a linear restoring force. Consequently, in the absence ofair resistance, objects in the tunnel will oscillate with SHM. Suppose an in- trepid astronaut exploring a 150-km-diameter, 3.5 X 1 0 kg asteroid discovers a tunnel through the center. If she jumps into the hole, how long will ti take her to fall all the way through the asteroid and emerge on the other side?
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We may see thousands of stars in the dark sky. Our universe consists of billions of stars. Stars may appear tiny to us but they are huge balls of gasses. Sun is a star of average size. Some stars are even a thousand times larger than the sun. The stars do not exist forever they have a certain lifetime. The life span of the sun is about 10 billion years. The star undergoes various changes during its lifetime, this process is called stellar evolution. The structure of the sun-like star is shown below.
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IIISuppose a large spherical object, such as a planet, with radius R and mass M has a narrow tunnel passing diametrically through it. A particle of mass m is inside the tunnel at a distance x less than or equal to R from the
center. It can be shown that the net gravitational force on the particlei s
due entirely to the sphere of mass with radius r ≤ ;x there is no net
gravitational force from the mass in the spherical shell with r > .x a. Find an expression for the gravitational force on the particle,
assuming the object has uniform density. Your expression will
be in terms of ,x R, m, M, and any necessary constants.
b. You should have found that the gravitational force is a linear restoring force. Consequently, in the absence ofair resistance, objects in the tunnel will oscillate with
asteroid discovers a tunnel through the center. If she jumps into the hole, how long will ti take her to fall all the way through the asteroid and emerge on the other side?
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