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3 years ago

Are dimensionless quantities always unitless

2 answers:

4 0

Important thing is that all unitless quantity is dimensionless quantity. .A dimensionless physical quantity may have an unit

arsen [322]3 years ago

4 0

Important thing is that all unitless quantity is dimensionless quantity. ... A dimensionless physical quantity may have an unit (e.g. Mechanical equivalent of heat) but a unitless physical quantity is always dimensionless (e.g. Coefficient of friction , refractive index

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The mean distance of an asteroid from the Sun is 2.98 times that of Earth from the Sun. From Kepler's law of periods, calculate

lutik1710 [3]

Answer:

The asteroid requires 5.14 years to make one revolution around the Sun.

Explanation:

Kepler's third law establishes that the square of the period of a planet will be proportional to the cube of the semi-major axis of its orbit:

$T^{2} = a^{3}$ (1)

Where T is the period of revolution and a is the semi-major axis.

In the other hand, the distance between the Earth and the Sun has a value of $1.50x10^{8} Km$ . That value can be known as well as an astronomical unit (1AU).

But 1 year is equivalent to 1 AU according with Kepler's third law, since 1 year is the orbital period of the Earth.

For the special case of the asteroid the distance will be:

$a = 2.98(1.50x10^{8}Km)$

$a = 4.47x10^{8}Km$

That distance will be expressed in terms of astronomical units:

$4.47x10^{8}Km.\frac{1AU}{1.50x10^{8}Km}$ ⇒ $2.98AU$

Finally, from equation 1 the period T can be isolated:

$T = \sqrt{a^{3}}$

$T = \sqrt{(2.98)^{3}}$

$T = \sqrt{26.463592}$

$T = 5.14AU$

Then, the period can be expressed in years:

$5.14AU.\frac{1yr}{1AU} ⇒ 5.14 yr$

$T = 5.14 yr$

Hence, the asteroid requires 5.14 years to make one revolution around the Sun.

8 0

3 years ago

Two resistors have resistances R(smaller) and R(larger), where R(smaller) < R(larger). When the resistors are connected in se

just olya [345]

Answer:

1.61ohms and 4.39ohms

Explanation:

According to ohm's law which States that the current (I) passing through a metallic conductor at constant temperature is directly proportional to the potential difference (V) across its ends. Mathematically, E = IRt where;

E is the electromotive force

I is the current

Rt is the effective resistance

Let the resistances be R and r

When the resistors are connected in series to a 12.0-V battery and the current from the battery is 2.00 A, the equation becomes;

12 = 2(R+r)

Rt = R+r (connection in series)

6 = R+r ...(1)

If the resistors are connected in parallel to the battery and the total current from the battery is 10.2 A, the equation will become;

12 = 10.2(1/R+1/r)

Since 1/Rt = 1/R+1/r (parallel connection)

Rt = R×r/R+r

12 = 10.2(Rr/R+r)

12(R+r) = 10.2Rr ... (2)

Solving equation 1 and 2 simultaneously to get the resistances. From (1), R = 6-r...(3)

Substituting equation 3 into 2 we have;

12{(6-r)+r} = 10.2(6-r)r

12(6-r+r) = 10.2(6r-r²)

72 = 10.2(6r-r²)

36 = 5.1(6r-r²)

36 = 30.6r-5.1r²

5.1r²-30.6r +36 =

r = 30.6±√30.6²-4(5.1)(36)/2(5.1)

r = 30.6±√936.36-734.4/10.2

r = 30.6±√201.96/10.2

r = 30.6±14.2/10.2

r = 44.8/10.2 and r = 16.4/10.2

r = 4.39 and 1.61ohms

Since R+r = 6

R+1.61 = 6

R = 6-1.61

R = 4.39ohms

Therefore the resistances are 1.61ohms and 4.39ohms

5 0

3 years ago

What is the lewis dot structure of Na+

SpyIntel [72]

The dots in the Lewis dot structure symbolize an atom's elements.
Since Na^+ is a positive ion (cation) with a charge of +1, it indicates that it has lost an electron. 
Since Na had one electron, to begin with, and it is now lost, Na^+ will have no dots. However, the charge must still be written as a superscript. 
Therefore, the Lewis dot structure for Na^+ is just Na^[+]

5 0

3 years ago

Which wave has a disturbance parallel to the wave motion

dem82 [27]

Answer:Surface wave

Explanation:

Longitudinal wave is perpendicular to the wave motion and transverse wave is the same as the wave motion

7 0

3 years ago

What is the formula for calculating density?

Sophie [7]

Density can be determined by the mass of an object and how much it takes up space (volume). It is represented by the formula D = M/V where D is the density in kg/m^3 or lb/ft^3, M is the mass in kg or lb and V is the volume in m^3 or ft^3. The answer would be A. For example, you are given the mass of an object of 40.5kg and a volume of 15m^3. Find its density.

D = M/V
D = (40.5 kg) / (15 m^3)
D = 27/10 or 2.7 kg/m^3

6 0

4 years ago

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Are dimensionless quantities always unitless​

Are dimensionless quantities always unitless