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**Imagine a tunnel that has been drilled through Earth: a**

smooth, straight tunnel with a frictionless interior .

The deepest point of the tunnel is at depth d, and the coordinate x

measures the distance along the tunnel from its deepest point to an

arbitrary point P a distance L from Earth's center. The known

parameters are the mass(Me) and radius of Earth(Re), as well as G.

Earth is assumed to have uniform density.

(a) What is the total mass of that portion of Earth that lies within

the distance L in termS of L, Me, Re. and G? (b) What is the grav-

itational force, in direction and magnitude, acting on a ball of

mass at point P? (c) What is the rotal force. in direction and magnitude. acting on the ball as a function of x and of the constants of the problem? Why is there no net force acting perpendicular to the tunnel? (d) What is the period of the motion if the ball

is released at rest at an entrance to the tunnel? Ignore air resistance. (e) What is the period of a satellite in circular orbit around

Earth at a radius equal to Earth's radius?

smooth, straight tunnel with a frictionless interior .

The deepest point of the tunnel is at depth d, and the coordinate x

measures the distance along the tunnel from its deepest point to an

arbitrary point P a distance L from Earth's center. The known

parameters are the mass(Me) and radius of Earth(Re), as well as G.

Earth is assumed to have uniform density.

(a) What is the total mass of that portion of Earth that lies within

the distance L in termS of L, Me, Re. and G? (b) What is the grav-

itational force, in direction and magnitude, acting on a ball of

mass at point P? (c) What is the rotal force. in direction and magnitude. acting on the ball as a function of x and of the constants of the problem? Why is there no net force acting perpendicular to the tunnel? (d) What is the period of the motion if the ball

is released at rest at an entrance to the tunnel? Ignore air resistance. (e) What is the period of a satellite in circular orbit around

Earth at a radius equal to Earth's radius?

**2. Harmonic, periodic motion and Gravity formulas**

**3. I'm at total loss**

**1. Homework Statement**

**2. Homework Equations**

**3. The Attempt at a Solution**