Question

III. Questions. Answer the following questions as best as you can. 1. Suppose that we can find a stable body of water big enough so that planetary Spherical bodies inside balloons can float or be submerged in the fluid. Which of the following planets would float? a. 55 Cancri e b. COROT-9b Mass: 5.1246x1025 kg Mass: 1.590x1027kg Radius: 1.387x10m Radius: 7.471x10m c. Saturn Mass: 5.6834x 1026kg Radius: 58,232km 2. What is meant when we say that if the frequency increases, the period decreases? Why must the period decrease? Explain.

Answer 1

1)

For a planet to float in water, buoyancy force on the planet must be greater than weight of the planet.

$W>F_B$,

that is   
Py Vg mg
(or)  
<A >m

a. 55 Cancri e

Volume

4 V =TR3 3 T(1.387 107)3 m3 3

PV 1000 (1.387* 107)3 1.118 1025 kg
and
m 5.1246 1025 kg

$\rho_w V<m$

Hence 55 Cancri e , cannot float on water.

b.COROT-9b

Volume

V =TR3 3 3 (7.471 107)3 m2

$\rho_w V=1000*\frac{4}{3}\pi (7.471*10^7)^3=1.747*10^{27}\,kg$ and

m1.590 1027 kq

<A >m

Hence COROT-9b​​​​​​​ , can float on water.

c)Saturn

Volume $V=\frac{4}{3}\pi R^3=\frac{4}{3}\pi (58232*10^3)^3\,m^3$

$\rho_w V=1000*\frac{4}{3}\pi (58232*10^3)^3=8.271*10^{26}\,kg$ and $m=5.16834*10^{26}\,kg$

<A >m

Hence Saturn​​​​​​​ , can float on water.

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2)

Frequency , is number of cycles undergone in unit time.

Period T, is the time taken to complete one cycle.

Frequency and period are inversely proportional.

$f=\frac{1}{T}$

As frequency increases, period decreases and vice versa.

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