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2 years ago

Select the correct answer.

Physics

1 answer:

anyanavicka [17]2 years ago

6 0

<h2>MULTIPLE CHOICES</h2>

$\large\mathcal{QUESTION:}$

What is the basic unit of all matter?

$\large\mathcal{CHOICES:}$

OA neutron
OB. atom
OC. electron
OD. proton
OE. nucleus

$\large\mathcal{ANSWER:}$

B. Atom

_____

<u>Atom</u> is the smallest, <u>indivisible unit of a chemical</u> <u>element and the fundamental unit of matter</u>. It consists of a nucleus (neutrons + protons) surrounded by an electron cloud. The <u>atom</u> is the smallest unit of matter that cannot be divided chemically and is a building block with its own set of properties.

<h3>#ProvideUniqueAnswers</h3>

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What is potential energy

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Three heavy rods are all made of the same uniform material. These rods have lengths 3 m, 4 m, and 5 m, and compose the sides of

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Answer:

[ 2.67 , 1 ] m

Explanation:

Given:-

- The side lengths of the rods are as follows:

a = 4 m , b = 4 m , c = 5 m

a = Base , b = Perpendicular , c = Hypotenuse

- All rods are made of same material with uniform density. With

Find:-

Find the coordinates of the center of mass of the triangle.

Solution:-

- The center of mass of any triangle is at the intersection of its medians.

- So let’s say we have a triangle with vertices at points (0,0) , (a,0) , and (0,b).

Median from (0,0) to midpoint (a/2,b/2) of opposite side has equation:

bx−ay=0

Median from (a,0) to midpoint (0,b/2) of opposite side has equation:

bx+2ay=ab

Median from (0,b) to midpoint (a/2,0) of opposite side has equation:

2bx+ay=ab

Solve all three equations simultaneously:

bx−ay=0 , bx = ay

ay + 2ay = ab , 3ay = ab , y = b/3

bx = b/3

x = a / 3

So the distance from the median to each leg of the triangle is 1/3 length of other leg.

- So the coordinates of the centroid for right angle triangle would be:

[ 2a/3 , b/3 ]

[ 2.67 , 1 ] m

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3 years ago

In a 2-dimensional coordinate system, the x- and y-axes are typically _____.

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3 years ago

A disk with radius R and uniform positive charge density s lies horizontally on a tabletop. A small plastic sphere with mass M a

Yanka [14]

Answer:

a. F = Qs/2ε₀[1 - z/√(z² + R²)] b. h = (1 - 2mgε₀/Qs)R/√[1 - (1 - 2mgε₀/Qs)²]

Explanation:

a. What is the magnitude of the net upward force on the sphere as a function of the height z above the disk?

The electric field due to a charged disk with surface charge density s and radius R at a distance z above the center of the disk is given by

E = s/2ε₀[1 - z/√(z² + R²)]

So, the net force on the small plastic sphere of mass M and charge Q is

F = QE

F = Qs/2ε₀[1 - z/√(z² + R²)]

b. At what height h does the sphere hover?

The sphere hovers at height z = h when the electric force equals the weight of the sphere.

So, F = mg

Qs/2ε₀[1 - z/√(z² + R²)] = mg

when z = h, we have

Qs/2ε₀[1 - h/√(h² + R²)] = mg

[1 - h/√(h² + R²)] = 2mgε₀/Qs

h/√(h² + R²) = 1 - 2mgε₀/Qs

squaring both sides, we have

[h/√(h² + R²)]² = (1 - 2mgε₀/Qs)²

h²/(h² + R²) = (1 - 2mgε₀/Qs)²

cross-multiplying, we have

h² = (1 - 2mgε₀/Qs)²(h² + R²)

expanding the bracket, we have

h² = (1 - 2mgε₀/Qs)²h² + (1 - 2mgε₀/Qs)²R²

collecting like terms, we have

h² - (1 - 2mgε₀/Qs)²h² = (1 - 2mgε₀/Qs)²R²

Factorizing, we have

[1 - (1 - 2mgε₀/Qs)²]h² = (1 - 2mgε₀/Qs)²R²

So, h² = (1 - 2mgε₀/Qs)²R²/[1 - (1 - 2mgε₀/Qs)²]

taking square-root of both sides, we have

√h² = √[(1 - 2mgε₀/Qs)²R²/[1 - (1 - 2mgε₀/Qs)²]]

h = (1 - 2mgε₀/Qs)R/√[1 - (1 - 2mgε₀/Qs)²]

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3 years ago