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Using dimensional analysis, construct a constant, with units of length only, out of all three of the following fundamental const

ludmilkaskok [199]

The quantity with units of length only is $\sqrt{\frac{hG}{c^3}}$

Explanation:

We have to combine the following constants:

- $h$ , Planck constant, with units $[m^2][kg][s^{-1}]$

- G, the Newton's gravitational constant, with units $[m^3][kg^{-1}][s^{-2}]$

- $c$ , the speed of light, with units $[m][s^{-1}]$

The combination of these constant should have units of length only, so with meters (m).

First, we notice that $h$ has [kg] in its units, while G has $[kg^{-1}]$ in its units, so in order to make the [kg] disappear, we have to multiply them and they should have same power, so:

$hG = [m^{2+3}][kg^{1-1}][s^{-1-2}]=[m^5][s^{-3}]$

Now we have to make the seconds, [s], disappear. We do that by dividing the new quantity by $c^3$ , so that the new units are:

$\frac{hG}{c^3}=\frac{[m^5][s^{-3}]}{([m][s^{-1}])^3}=\frac{[m^5][s^{-3}]}{[m^3][s^{-3}]}=[m^2]$

We are almost done: now the quantity has units of an area, squared meters. Therefore, in order to make it have it units of length, we just take its square root:

$\sqrt{\frac{hG}{c^3}}=\sqrt{[m^2]}=[m]$

Learn more about gravitational constant:

brainly.com/question/1724648

brainly.com/question/12785992

#LearnwithBrainly

4 0

3 years ago

How do you find speed of a ball at maximum height

Crazy boy [7]

Explanation:

At maximum height, the vertical component of a ball's speed is 0. So the net speed is equal to whatever the horizontal component of the ball is. If the ball is launched straight up, the speed at the highest point is simply 0.

5 0

3 years ago

Argon, atomic number 18, has an atomic weight of 39.9. Potassium, atomic number 19, has an atomic weight of 39.1. Which of these

Rufina [12.5K]

Answer: D

Explanation:

Atomic weight is measured by adding the number of protons and neutrons in an atom's nucleus. Argon's atomic number is 18 while potassium's is 19. This means that Argon will always have 18 protons while potassium will always have 19 protons.

To make the numbers easier to work with, round each atomic weight. We'll say the atomic weight of potassium is 39 and the atomic weight of argon is 40. To see how many neutrons each one has, I can set up a simple equation for each using the following equation:

Atomic weight = protons + neutrons

Potassium:

39 = 19 + N --> N = 20

Argon:

40 = 18 + N --> N = 22

An atom is defined by the number of protons it has, but the number of neutrons can vary. We call these isotopes, or atoms with the same number of protons but a different number of neutrons. As the math shows, argon typically has more neutrons per atom than potassium does.

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3 years ago

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Which branch of science involves the study of matter and energy

Olin [163]

Physics<span> is a natural science that involves the study of matter and its motion through space time, along with related concepts such as energy and force.</span>

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3 years ago

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Explain how characteristic and traits are related<br>

jok3333 [9.3K]

Traits are basically your phenotype. They include things like hair color, height, and eye color. Alleles are versions of genes. ... This is a pretty basic idea of how traits and alleles are related.

4 0

3 years ago