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Classical Mechanics Level 4

A tube is drilled between two points (not necessarily diametrically opposite) on the earth. An object is dropped into the tube.

How much time does it take to reach the other end?

Ignore friction, and assume that the density of the earth is constant.

Find the time in minutes.

Radius of the earth = 6.38 × 1 0 6 m =6.38 \times 10^6 m

Mass of the earth = 5.98 × 1 0 24 k g =5.98 \times10^{24}kg

G = 6.67 × 1 0 − 11 m 3 k g ⋅ s 2 G=6.67 \times 10^{-11}\frac{m^3}{kg \cdot s^2}


The answer is 42.

Pratik Shastri by Pratik Shastri , 35, India

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1 solution

I used this formula:

− ω 2 R = − G M R 2 -\omega ^ {2} R = -\frac{GM}{R^{2}}

ω = G M R 3 \omega = \sqrt{\frac{GM}{R^{3}}}

t = π ω t = \frac{\pi}{\omega}

t = π R 3 G M t = \pi \sqrt{\frac{R^{3}}{GM}}

Subsitute, and we get

t ≈ 42 t \approx \boxed{42}

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