Suppose, a tunnel is made along the diameter of Earth and we drop a ball inside it. How will the ball behave? Please help me understand.
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It will oscillate around the center of Earth. To find the equation you will need to solve the generic oscillation problem: the gravity force / acceleration depends on the distance to Earth's center while everything which is further from the center will not impact on the acceleration.
- $g(x)=G\cdot M(x)/x^2$;
- $M(x)=\mathrm{average~earth~density}\cdot 4/3\cdot \pi \cdot x^3$
- $g(x)=-\omega^2\cdot x$
I let you to calculate the rest.
