1.) a particle is dropped in to a hole drilled straight through the center of ea

Question

1.) a particle is dropped in to a hole drilled straight through the center of earth. Neglecting rotational effects, show that the particles motion is simple harmoic if you assume earth has a unifrom density. Show that the period of oscillation is 84 min.

2.) assuming that the air resistance is not important, calculate the minimum velocity a particle must have at the surface of Earth to escape from earth's gravitational field. Obtain a numerical value for this result. Do you know what is this velocity called?

Explanation / Answer

1. accn. inside earth = GMx/R^3 at distance x ....

so it is SHM as a is prop. to x .... => w= sqrt (GM/R^3) =84 min.

2. this vel. is called escape velocity ...

for escaping earth ... its total energy shud be 0 ..

=> .5mv^2 = GMm/R => v = sqrt(2GM/R) ... M--- mass of earth ...

v =11.2 km/s

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