In the approximation that a planet is a sphere of uniform density, it can be sho

Question

In the approximation that a planet is a sphere of uniform density, it can be shown that the gravitational force it exerts on a mass m inside the planet at a distance r from the center is mg(r/R), where R is the radius of the planet, and g is the magnitude of the gravitational field near the surface of that particular planet. (Note that at the surface, the force is indeed mg, and at the center it is zero). Consider a planet of mass 6.00 times 10^24kg and radius 6.00 times 10^6 m. (Use G = 6.67 times 10^-11 N middot m^2/kg^2.) What is the value of g for this planet? 11.1 N/kg Suppose that there was a hole drilled along a diameter straight through a planet and the air was pumped out of the hole. If an object was released from one end of the hole, how long would it take to reach the other side of the planet? 5002.6 s What will happen when the object reaches the other side of the planet?

Explanation / Answer

period of oscillation = 2Pi *sqrt( R/g)

T = 2Pi*Sqrt(6*10^6/11.1)

T = 4619.48 sec

time taken to reach from end to other end = T/2 = 4619.48/2=2309.74 sec

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