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Jupiter is the largest planet in our solar system, having a mass and radius that are, respectively, 318 and 11.2 times that of earth. Suppose that an object falls from rest near the surface of each planet, and that each object falls the same distance before striking the ground. Determine the ratio of the time of fall on Jupiter to that on earth.

Sagot :

Manetho

Answer:

0.62

Explanation:

we know that [tex]g=\frac{G M}{R^{2}}[/tex]

[tex]\frac{g_{g}}{g_{J}}=\frac{M_{g}}{M_{J}} \times \frac{R_{j}^{2}}{R_{z}^{2}}=\frac{M}{318 M} \times \frac{(11.2)^{2} R_{g}^{2}}{R_{g}^{2}}[/tex]

[tex]\frac{g_{g}}{g_{j}}=\frac{125.44}{318}=0.394[/tex]

We know that  [tex]=\sqrt{\frac{2 h}{g}}[/tex]

here given that each object falls the same distance

[tex]\therefore t \alpha \sqrt{\frac{1}{g}}[/tex]

[tex]\therefore \frac{t_{J}}{t_{B}}=\sqrt{\frac{g_{g}}{g_{J}}}=\sqrt{\frac{g}{0.394}}[/tex]

[tex]\therefore \frac{t_{j}}{t_{g}}=\sqrt{0.394}=0.62[/tex]

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