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zzz [600]
4 years ago
10

Consider two planets with uniform mass distributions. The mass density and the radius of planet 1 are rho1 and R1, respectively,

and those of planet 2 are rho2 and R2. What is the ratio of their masses?
Physics
1 answer:
spin [16.1K]4 years ago
7 0

Answer:

\frac{R_1^3 * \rho _1}{R_2^3 * \rho _2}

Explanation:

The mass density of an object with uniform mass distribution its defined as

\rho = \frac{mass}{volume}.

So, if we know the volume, and, we can obtain the mass of the object:

mass = volume * \rho.

Now, we can take the planets as spheres, of course, this is only an approximation, but good enough for us. The volume of a sphere of radius r its:

Volume_{sphere} = \frac{4}{3} \pi r^3

So, for our planets, the mass its given by:

mass = volume * \rho\\mass = \frac{4}{3} \pi r ^3 \rho,

so

mass_{planet1} = \frac{4}{3} \pi R_1^3 \rho_1

mass_{planet2} = \frac{4}{3} \pi R_2^3 \rho_2

Now, we can take the ratio:

\frac{mass_{planet1}}{mass_{planet2}} = \frac{ \frac{4}{3} \pi R_1 ^3 \rho_1 }{ \frac{4}{3} \pi R_2 ^3 \rho_2 }

Now, we can just cancel the \frac{4}{3} \pi [\tex] that appear in both sides of our fractions, and finally obtain: [tex]\frac{R_1^3 * \rho _1}{R_2^3 * \rho _2}.

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4 years ago
Two charges are located in the xx–yy plane. If q1=−4.10 nCq1=−4.10 nC and is located at (x=0.00 m,y=1.080 m)(x=0.00 m,y=1.080 m)
Gala2k [10]

Answer:

Explanation:

Due to first charge , electric field at origin will be oriented towards - ve of y axis.

magnitude

Ey = -8.99 x 10⁹ x 4.1 x 10⁻⁹ / 1.08² j

= - 31.6 j N/C

Due to second charge electric field at origin

= 8.99 x 10⁹ x 3.6  x 10⁻⁹ / 1.2²+ .6²

= 8.99 x 10⁹ x 3.6  x 10⁻⁹ / 1.8

= 18 N/C

It is making angle θ where

Tanθ = .6 / 1.2

= 26.55°

this field in vector form

= - 18 cos 26.55 i - 18 sin26.55 j

= - 16.10 i - 8.04 j

Total field

= - 16.10 i - 8.04 j + ( - 31.6 j )

= -16.1 i - 39.64 j .

Ex = - 16.1 i

Ey = - 39.64 j .

8 0
4 years ago
As the wavelength of an electromagnetic wave ___ the frequency of the wave ________.
adoni [48]

Answer:

As the wavelength of an electromagnetic wave _decrease__ the frequency of the wave _increase_______.

Explanation:

What is the relationship between frequency and wavelength?

Wavelength and frequency of light are closely related. The higher the frequency, the shorter the wavelength. Because all light waves move through a vacuum at the same speed, the number of wave crests passing by a given point in one second depends on the wavelength.

That number, also known as the frequency, will be larger for a short-wavelength wave than for a long-wavelength wave. The equation that relates wavelength and frequency is:

V= fλ

where v= velocity

           f= frequency

            λ = wavelength

⇒ f = v/λ  

also f ∝ 1/λ

For electromagnetic radiation, the speed is equal to the speed of light, c, and the equation becomes:

C= fλ

where c= Speed of light

           f= frequency

            λ = wavelength

⇒ f = v/λ  

also f ∝ 1/λ

8 0
4 years ago
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