Several volcanoes have been observed erupting on the surface of one of Jupiter's closest moons. Suppose that material ejected from one of these volcanoes reaches a height of 5.10 km after being projected straight upward with an initial speed of 132 m/s. Given that the radius of this particular moon is 2000 km, calculate its mass. (in kg)

1.025*10^23 kg

Explanation:

Given

Height of eruption, h = 5.1 km

Initial speed of the material, v = 132 m/s

Radius of moon, r = 2000 km

Mass of the moon, m = ?

We would solve this by using the formula

g = GM/r²

Also, we know that

h = v²/2g, substituting the formula of g into this equation, we have

h = v²/2(GM/r²)

h = v²r² / 2GM

Since we are looking for the mass, we make m the subject of formula, so that

M = v²r² / 2Gh

Now, substituting all the values, we get

M = [132² * (2000*10^3)²] / 2 * 6.67*10^-11 * 5.1*10^3

M = (17424 * 4*10^12) / 6.8*10^-7

M = 6.97*10^16 / 6.8*10^-7

M = 1.025*10^23 kg

Thus, the mass of the moon is 1.025*10^23 kg

scattering of light by tiny particles in air to produce the colors we see on sky, is dependent on the following factors:

(i) wavelength of light

(ii) size of the scattering particle  

(iii) distance traveled by light through the atmosphere.

according to rayleigh's law of scattering, the amount of scattering is inversely proportional to the fourth power of its wavelength. shorter the wavelength, greater is its scattering. hence violet/blue light is scattered more than red.

sun's light is a composite light ( visible light) with wavelengths in the range 400 nm (violet) to 700 nm (red). as sunlight passes through our atmosphere, the molecules of air scatter light according to their wavelengths. during sunrise and sunset, the sun's position is below the horizon. hence light from the sun travels a greater distance in the atmosphere when compared to its position a noon.

as sunlight enters the earth's atmosphere, blue light is scattered away and at the end of its journey in the sky, only red and orange wavelengths remain in the beam.

hence at sunrise and sunset, the sky appears reddish orange.

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