Which formula represents Gay-Lussac’s law?

xz_007 [3.2K]

a) The x-coordinate of the center of gravity is $\frac{19}{18}\cdot a$ .

b) The y-coordinate of the center of gravity is $\frac{19}{18}\cdot a$ .

<h3>Determination of the coordinates of the center of gravity</h3>

Let suppose that each square has an <em>uniform</em> density, the coordinates of the center of gravity of each square with respect to the origin are, respectively:

$\vec r_{1} = (0.5\cdot a, 0.5\cdot a)$

$\vec r_{2} = (1.5\cdot a, 0.5\cdot a)$

$\vec r_{3} = (0.5\cdot a, 1.5\cdot a)$

$\vec r_{4} = (1.5\cdot a, 1.5\cdot a)$

The center of gravity of the <em>entire</em> system is found by applying definition of <em>weighted</em> averages:

$\vec r_{cg} = \frac{W_{1}\cdot \vec r_{1}+W_{2}\cdot \vec r_{2}+W_{3}\cdot \vec r_{3}+W_{4}\cdot \vec r_{4}}{W_{1}+W_{2}+W_{3}+W_{4}}$

Where $W_{1}$ , $W_{2}$ , $W_{3}$ and $W_{4}$ are weights of the each square, in newtons.

Now we proceed the coordinates of the center of gravity of the entire system:

$\vec r_{cg} = \frac{(50\,N)\cdot (0.5\cdot a, 0.5\cdot a) + (30\,N)\cdot (1.5\cdot a, 0.5\cdot a)+(30\,N)\cdot (0.5\cdot a, 1.5\cdot a)+(70\,N)\cdot (1.5\cdot a, 1.5\cdot a)}{50\,N+30\,N+30\,N+70\,N}$

$\vec r_{cg} = \frac{5}{18}\cdot (0.5\cdot a, 0.5\cdot a) +\frac{1}{6}\cdot (1.5\cdot a, 0.5\cdot a) +\frac{1}{6}\cdot (0.5\cdot a, 1.5\cdot a) + \frac{7}{18}\cdot (1.5\cdot a, 1.5\cdot a)$

$\vec r_{cg} = \left(\frac{19}{18}\cdot a, \frac{19}{18}\cdot a \right)$ $\blacksquare$

a) The x-coordinate of the center of gravity is $\frac{19}{18}\cdot a$ . $\blacksquare$

b) The y-coordinate of the center of gravity is $\frac{19}{18}\cdot a$ . $\blacksquare$

To learn more on center of gravity, we kindly invite to check this verified question: brainly.com/question/20662119

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C) has the most mass

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If a magnetic field is to exert a force on a current-carrying wire, the field must have some vector component:

mash [69]

Answer:

D.) perpendicular to the current

i am 100% sure :)

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How did the sun moon and the earth make seasons?

lisov135 [29]

<span>Seasons happen because Earth's axis is tilted at an angle of about 23.4 degrees and different parts of Earth receive more solar energy than others.</span>

4 0

3 years ago

You are given a copper bar of dimensions 3 cm × 5 cm × 8 cm and asked to attach leads to it in order to make a resistor. If you

Nataliya [291]

Answer:

Option B is correct.

The leads should be attached to the opposite faces that measure 3 cm × 5 cm to obtain the maximum possible resistance.

Explanation:

The resistance of a material is given by

R = (ρL)/A

where ρ = resistivity of the material

A = Cross sectional Area through which current would flow

L = length of the material.

From the relation, it is evident that the resistance of a material is directly proportional to its length and inversely proportional to its cross sectional Area.

As the length of material increases, the resistance of the material also increases, and a decreasing length translates to a decreasing resistance too. (Direct Proportionality)

And as the cross sectional Area of the material increases, the resistance of the material decreases. Decrease in cross sectional Area of the material translates to an increase in resistance. (Inverse Proportionality)

To maximize resistance of a material, it would make sense to maximize the length and minimize the cross sectional Area of that material. (Since resistivity is assumed to be constant)

And with a dimension of (3 × 5 × 8), the longest length is 8 cm and the smallest cross sectional Area is (3 × 5).

So, the leads should be atrached to the face with area (3 cm × 5 cm), which is the smallest cross sectional Area and gives the largest length between the faces (8 cm).

This subsequently maximizes the resistance.

Hope this Helps!!!

4 0

3 years ago

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