I need part A, B and C of this problem. Consider a spherical planet of radius R

Question

I need part A, B and C of this problem.

Consider a spherical planet of radius R and mass M. The planet has uniform density. A 33% Part (a) Someone has drilled a hole straight through the center of this planet to the other side and is about to drop a small object of mass into the hole. We can show that the object will experience simple harmonic motion in the hole by showing that the gravitational force on the object will obey Hooke's law, F_grav = -kx, where k is the force constant and x denotes the displacement from equilibrium position, which is the planet's center. Enter an expression for k, in terms of R, M, m, and the gravitational constant, G. (b) When the object is dropped into the hole, what will be its period of oscillation, in seconds, if R = 5 times 10^6 m and M = 6 times 10^24 kg? A 33% Part (c) What would be the period of oscillation, in seconds, if the planet were Earth? The radius of Earth is 6.38 times 10^6 m and its mass is 5.9 times 10^24 kg. Assume the mass is distributed uniformly.

Explanation / Answer

a) F = G*m M*r/R^3

k=GMm/(R^3)

b) T= 2pi sqrt(m/k) = 2 pi sqrt( R^3/GM)= 3511.52 seconds

c) T= 5104.13 seconds=

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---