What is the
law of universal gravitation?

The example of mass and weight being proportional is Force = mass * acceleration.

The proportionality can be direct or inverse proportionality.

Direct proportionality can be defined as the increase in the second quantity if there is an increase in the first quantity when both quantities are related.

Inverse proportionality can be defined as a decrease in the second quantity when the first quantity is increased when both quantities are related.

Mass and weight are proportional to each other.

For that we can consider the example given below:

weight is the force exerted by the earth's gravity on the particle.

we know that

force = Mass * acceleration

as weight = force

weight = mass * acceleration

so if the acceleration is constant the increasing weight mass also increases.

so at constant acceleration weight and mass are directly proportional.

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An interior designer is choosing a paint color for a room and has two samples that are both blue, however one blue is described as brighter than the other. Both would have the same wavelength but would differ due to the amplitude property of light.

The amplitude plays an important part in differentiating the same colors of the same wavelength. It tells us about the brightness or intensity of a certain light wave as compared to others of the same wavelength. So, whenever two same colors look different due to brightness, it is due to the amplitude property of the light.

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Resolving power is most improved by increasing the distance between telescopes.

Relatively close objects, such binary stars or individual galaxies’ stars, occupy very small angles on telescopes. We require really huge apertures to resolve them. The resolving power of telescope is calculated by Rayleigh's formula,

∆ θ = 1.22λ/d

So, resolving power = 1/∆θ = d/1.22λ

The reciprocal of the smallest angle occupied at the telescope’s objective lens by two point objects that can just be recognised as distinct is the definition of a telescope’s resolving power.

A telescope Is an optical equipment that uses lenses, curved mirrors, or a combination of the two to view distant objects. Other tools can be used to view distant objects by their electromagnetic radiation emission, absorption, or reflection.

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The ball rises 53.361 m above the point where the bat hit the ball.

When a batter hits a ball high in a baseball game, the ball remains in the air for 6.6 seconds.

The acceleration of gravity is 9.8 m/s².

The vertex value of time is half of 6.6 seconds or 3.3 seconds.

Therefore, the final velocity at the maximum height is v = 0 m/s

Now, using the equation of motion:

v - u = gt

v = u + gt

u × sin(θ) = - gt

u × sin(θ) = 9.8 × 3.3

u × sin(θ) = 32.34 m/s

Now, by using the equation of motion:

v² - u² = 2gh

h = ( v² - u²) / 2g

h = ( 0 - (32.34)² ) / 2(9.8)

h = (1045.8756) / 19.6

h = 53.361 m

The ball rises 53.361 meter high.

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Answer:Apparently the further displacement should be of other 3 cm; but, let's consider the development of the spring on one vertical plain, and fixed on a wall by the upper end.

Now the spring doesn't look circular; but as a stick fixed on the wall. Before placing the first 100 grams weight, the stick is not horizontal; but its overhanging end is lower by the measured length of the spring at rest. The length line of the spring with its horizontal projection line forms an angle.

The first 100 grams load is decomposed in function of the new angle: one component in line with the stick, the other one perpendicularly respect to it. The same happens with 200 grams.

The flection momentum is given by the perpendicular component of the load with respect to the stick line in overload, and the measure of the stick itself. Such component is inversely proportional to the other component, and decreases in relation to higher load while the other component (that doesn't produce flexion) encreases.

I assume that I can't calculate the new displacement because is not given the height of the spring at rest, the length of the development of the spring. Accordingly, I cannot calculate all various angles of the stick in relation with gravity.

Explanation:

When a 25 g mass is attached to the same spring, the spring is stretched by 2 cm.

Hooke's law states that the applied force [F] equals a constant k times the displacement or change in length [x].

Mathematically - F = - Kx

Given is a situation in which a stretch of 8 cm is caused by a 100g mass.

From this, we can write -

Mass [m] = 100 g = 0.1 Kg

Displacement [x] = 8 cm = 0.08 m

According to the question -

The spring constant [K] can be calculated using Hook's law as -

F = -Kx

mg = -Kx

K = - mg/x

K = - (0.1 x 9.8) / 0.08

K = - 12.25 N/m

|K| = 12.25 N/m

Now, when mass [M] = 25g = 0.025 Kg, using Hook's law -

|F| = |- kx| = kx

Mg = 12.25x

x = Mg/12.25

x = (0.025 x 9.8)/12.25

x = 0.02

x = 2 cm

Therefore, when a 25 g mass is attached to the same spring, the spring is stretched by 2 cm.

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When performing a voltage drop test on a 12v blower motor circuit, the reading is 2.7 volts across the fan switch when closed. the maximum voltage available at the fan is

V=9.3 volts

This is further explained below.

Generally, Electric potential difference, also known as voltage, electric pressure, or electric tension, is the amount of labor required per unit of charge to transfer an electrostatic test charge from one location to another.

In conclusion, When testing the voltage drop across the fan switch on a circuit with a 12v blower motor, the measurement is 2.7 volts. V=9.3 volts is the maximum power supply for the fan.

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Kepler used the extensive records of planetary positions measured by  Tycho to discover that the orbits of the planets are elliptical.

The planets would be listed from smallest to largest in order of size: Mercury, Mars, Venus, Earth, Neptune, Uranus, Saturn, and Jupiter. The gas giants are Jupiter and Saturn, whereas the more distant Uranus and Neptune are known as the ice giants.

The International Astronomical Union (IAU) downgraded Pluto to a dwarf planet since it failed to satisfy all three criteria for a full-sized planet. Pluto essentially meets all the criteria, with the exception of the one that it "has not cleared its nearby vicinity of other objects."

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Answer: B

Explanation:

The deflecting electric field is 0.83mv/m

Acc. to the newtons 2nd law - there is an acceleration when a force acts on an object.

F = ma     (equation 1)

where

F is force

m is mass of object

a is acceleration

Electric field intensity- it is defined as force experienced by a unit positive charge placed at that point.

it is denoted by E = F/q

where

F is force

q is the charge

F = Eq     (equation2)

from 1 and 2 equation we get

ma = Eq

E = ma /q

Charge on the drop of ink.is q.

(e is the charge on an electron.)

so,

q = 751896×e

q = 751896×1.6 ×⁻¹⁹

q = 12.03 ×10⁻¹⁴

m = 10⁻¹¹kg

a = 10⁴ m/s²

using above values

E = ma /q

E = 10⁻¹¹×10⁴/12.03 ×10⁻¹⁴

E = 0.83mv/m

The deflecting electric field is 0.83mv/m

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The frictional force acting on the block is completely static in nature and is equal to 90 Newton's.

Friction is a force that acts opposite to the direction of motion of body in order to oppose its motion.

Given in the question is a box of weight 120 N initially resting on a horizontal table. From the data given, we can write -

Weight of box [W] = 120 Newton

Coefficient of static friction (μ[s]) = 0.75

Coefficient of Kinetic friction (μ[k]) = 0.40

Horizontal push (F[h]) = 84 N

The frictional force is given by -

For Static friction - F[s] = μ[s] N

For Kinetic friction - F[k] = μ[k] N

Now, initially the box is at rest. When a horizontal force of 84 Newton is applied on it, the static friction will try to oppose the motion. For forward motion of the block -

F[h] - F[s] ≥ 0

F[h] - μ[s] N ≥ 0

84 - 0.75 x 120 ≥ 0            (Normal Reaction [N]  = Weight)

84 - 90 ≥ 0

- 6 ≥ 0

which is false.

This means that the static frictional force is greater than horizontal push and opposes the motion. The force due to static friction will only exist since, the body was able to move, so kinetic friction is of no use here.

So, the frictional force on the block will be = F[s] =  μ[s] N = 90 Newtons.

Therefore, the frictional force acting on the block is completely static in nature and is equal to 90 Newton's.

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The direction of the apple is 78.5 degrees.

We know that force is that which brings about motion. Force acts on an object when it is stationary and makes it to move or makes a moving object to change direction.

The magnitude and the direction of the vector is regarded as very important when we are trying to solve for a particular vector.

Now  we can see that the force of gravity acts vertically while the force that is exerted by the wind acts horizontally. This implies that we now have  right angled triangle and the direction of the force could be obtained geometrically as;

tan^-1(9.16 N/ 1.87 N)

= 78.5 degrees

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Answer: 1. -15m/s

2. -37.5m

Explanation:

1. -3m*5=-15m/s

2. v=velocity. d=displacement. t=time. a=acceleration

d=vt+(1/2)at^2

d=0*5+(1/2)(-3)(5)^2   ==> car was at rest before accelerating

d=0+(1/2)(-3)(25)

d=(1/2)(-75)

d=-37.5 meters

The magnetic field lines of the magnetized iron ring are concentrated near the north and south poles of the ring.

When an iron ring is put near the north pole of a bar magnet, the bar magnet's magnetic field lines are drawn to it. As a result, the iron ring gets magnetic, and its field lines become concentrated towards the ring's north and south poles.

By matching the north pole of the iron ring with the north pole of the bar magnet, the iron ring is magnetized. This produces a strong magnetic field between the two poles, magnetizing the iron ring. The iron ring's magnetic field lines will be visible as a series of concentric circles around the bar magnet's north pole.

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The property of the rock that will change if it is transported from the moon to the earth, is the weight.

The weight of an object is directly proportional to the action of gravity on the mass of that object. It can be confirmed with the weight formula:

W = m * g

Where:

By contrast, the mass of an object indicates the amount of matter it contains, it is a constant magnitude.

It is the physical magnitude that expresses the force exerted by gravity on the mass of a body, this is expressed in units of the international system in Newton.

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The mass of an object that requires 15.0N to accelerate it at rate of 3 m/s² is 1.17 kg.

The mass of an object is the quantity of matter present in an object.

The mass of an object is related to its acceleration and the applied force by the given formula below:

force = mass * acceleration

mass = force/acceleration

From the data provided:

force applied = 15.0 N

acceleration = 3 m/s²

The force applied overcomes the weight of the body.

Total force applied = weight + net force

Total force = mg + ma

Total force = m(g + a)

m = force/(g + a)

mass = 15(9.8 + 3)

m = 1.17 kg

Therefore, the mass of the object is 1.17 kg.

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The distance covered by man was 20 km, his total displacement would be 14.14 km and the angle of his displacement would be 45° compared to the north.

Displacement is defined as changes in an object's position referred to as displacement. It is a vector quantity that has both a direction and a magnitude.

As per the given condition,

Distance covered by man = 10 km + 10 km = 20 km

Total displacement will be the hypotenuse of two north and west sides.

⇒ Total displacement = √(10²+10²)

⇒ Total displacement = √(100+100)

⇒ Total displacement = √200

⇒ Total displacement = 10√2

⇒ Total displacement = 14.14 km

The angle of his displacement would be : tan⁻¹(10/10) = 45°

Hence, the distance covered by the man was 20 km, his total displacement would be 14.14 km and the angle of his displacement would be 45° compared to the north.

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Answer: The charges must be like charges (both positive or both negative).

Explanation:

During its downward journey at point b, its kinetic and potential energies will be mgh and 6gx respectively.  

Kinetic energy will be mg × ( total height = x ) and potential energy will be 6 g x. Let's assume that point B is located at  height x unit from the surface,

As we know , potential energy = m g h ( where m = mass of the body , g = gravitational acceleration and h = height from the surface )

so potential energy at point A = 480 j  or 6gh ( h = total height from surface )and for the point B it is , 6gx ( where g = 9.8 m/s²) .

At point A , total kinetic energy is 0 or, 1/2 mu² = 0

∵ u = 0,

So, initial velocity is zero ,

Now we will apply Newton's formula ,

and we will get , v² = u² + 2as

or, v² = 0 + 2 g h ( as acceleration = gravitational acceleration = g ; s = height h )

[ multiplying both side with 1/2 m ]

or , 1/2 m v² =  m g h

Kinetic energy = 1/2 m v² = m g h

[ h = ( total height - x )  at point B .  ]

Kinetic energy = m g ( total height - x ).

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The de - acceleration of bullet from 360 m/s after it struck the tree trunk and was brought to rest is -152.54 x 10⁴ m/s².

Acceleration is defined as the rate of change of velocity with respect to time. Mathematically -

Given is a bullet initially travelling at 360 m/s struck into a tree trunk 8.5 cm inside and comes to rest. From this, we can write

initial velocity [u] = 360 m/s

final velocity [v] = 0 m/s

distance travelled [d] = 8.5 cm = 0.085 m

The time span after which bullet comes to rest will be -

Δt = d/u

Δt = 0.085/360 = 2.36 x 10 ⁻⁴ seconds

a = Δv/Δt

Δv = 0 - 360 = - 360 m/s

a = (v - u)/Δt

a = - 360/(2.36 x 10 ⁻⁴)

a = - 152.54 x 10⁴ m/s²

Therefore, the de - acceleration of bullet from 360 m/s after it struck the tree trunk and was brought to rest is -152.54 x 10⁴ m/s².

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Answer:d=80,001 m

Explanation:df = di + Vave(t)

d = 0 + 300,000,000(0.00026667)

d = 80,001 m

Because protons and electrons in an atom carry opposite charges, they are attracted to each other and thus maintain the boundaries of the atom as a  singular closed system.

An atom consist of equal number of electrons and protons, due to which the attractive force between them binds the atom together and hence no exchange of matter takes place, therefore an atom posses closed system.

If we consider that energy is emitted, when electrons emit energy, then this energy is absorbed in the atom, thus preventing the electrons from hitting the nucleus. More specifically, as the electron wave travels around the nucleus, it emits energy, but this energy is recaptured when the wave doubles back on itself in 1/2 or full wavelengths to form a standing wave.

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The mass of the electric car moving at the given speed and kinetic energy is determined as 920 kg.

The kinetic energy of an object is the energy possessed by the object due to the motion of the object. The kinetic energy of an objects is determined from the product of object's mass and its velocity.

The mass of the electric car is calculate by applying kinetic energy formula as follows;

K.E = 0.5 mv²

where;

Substitute the given parameters and solve for the mass of the electric car.

m = (K.E)/(0.5v²)

m = (222640) / (0.5 x 22²)

m = 920 kg

Thus, the mass of the electric car moving at the given speed and kinetic energy is determined as 920 kg.

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A. Another conclusion that can be drawn from the student experiment is the ball stops because there is some force acting on it.

There are several forces that will act on an object moving on an inclined plane. These forces include the following;

When the object is moving up, gravitational force will tend to pull the object downwards and the frictional force will tend to oppose this downward motion of the object.

When the object is rolled down the plane, gravitational force tends to aid the motion of the object while frictional force tends to slow the object down.

Eventually, the object stops because the frictional force opposing the object motion is greater than the gravitational force pushing the object downwards.

Thus, another conclusion that can be drawn from the student experiment is the ball stops because there is some force acting on it.

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Given Quantity

v esc =1.12×10 4  m/s: escape speed from the Earth =1.12×10  m/s: escape speed from the Earth

m = 2(1.66 \times 10^{-27}) = 3.32 \times 10^{-27}{kg}m=2(1.66×10 −27)=3.32×10 −27 kg: molecular mass of helium

We calculate the temperature at which helium atoms has an rms speed equal to the escape speed.

The rms speed is equal to the following

v rms​  = 3kT/m​ ​ (1)

where kk is the Boltzmann constant, TT is the temperature, and mm is the molecular mass.

Manipulating Equation (1)(1) to be equal to the escape speed, we can calculate the temperature to be

v esc= 3kT/m esc

​v esc= = 3kT/m esc

Tesc=mv2esc/3k

What is gravitational field?

A gravitational field is a framework used in physics to explain the effects that a large thing has on the area surrounding it, exerting a force on smaller, less massive bodies. As a result, a gravitational field, which is measured in n. per kilogram, is employed to describe gravitational phenomena.

Therefore,

the escape speed from the earth is 1.12 ⇥104 m s 1, so that a gas molecule travelling away from the earth near the outer boundary of the earth’s atmosphere would, at this speed, be able to escape from the earth’s gravitational field and be lost to the atmosphere. at what temperature is the average speed of (a) oxygen molecules, and (b) helium atoms equal to 1.12 ⇥104 m s 1? (c) can you explain why our atmosphere contains oxygen but not helium?

Given Quantity

v esc =1.12×10 4  m/s: escape speed from the Earth =1.12×10  m/s: escape speed from the Earth

$ k= 1.38 \times 10^{-3}$: Boltzmann constant

m = 2(1.66 \times 10^{-27}) = 3.32 \times 10^{-27}{kg}m=2(1.66×10 −27)=3.32×10 −27 kg: molecular mass of helium

We calculate the temperature at which helium atoms has an rms speed equal to the escape speed.

The rms speed is equal to the following

v rms​  = 3kT/m​ ​ (1)

where kk is the Boltzmann constant, TT is the temperature, and mm is the molecular mass.

Manipulating Equation (1)(1) to be equal to the escape speed, we can calculate the temperature to be

v esc= 3kT/m esc

​v esc= = 3kT/m esc

Tesc=mv2esc/3k

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​

Statement 1 and 3 are correct.

According to Ohm's law,

P = V I

V = I R

where,

P = Power

V = Voltage

I = Current

R =Resistance

Given that,

P = 250 * [tex]10^{-3}[/tex] W

If R = 10 Ω

P = [tex]I^{2}[/tex] R

[tex]I^{2}[/tex] = P / R

[tex]I^{2}[/tex] = 250 * [tex]10^{-3}[/tex] / 10

I = 15.81 * [tex]10^{-2}[/tex] A

V = 15.81 * [tex]10^{-2}[/tex] * 10

V = 1.581 V < 50 V

So statement 1 is correct

If the same method is applied for 100 Ω, the voltage would be 50 V which is greater than 5 V. So statement 2 is wrong

V = P / I

V = P R / V

V = [tex]\sqrt{0.25*R}[/tex]

According to this, statement 3 is correct and statement 4 is wrong.

Ohm's law states that, when two points have a potential difference, the current passing through the resistance is directly proportional to the voltage across the two points.

The given question is incomplete. The complete question is :

The power rating of the resistors in our kits are 1/4 watt. That means the power dissipated by any resistor of resistance R should not exceed 250 mW. Using the power formula P = Vxl and Ohm's law, which of the following is true? V is the voltage across the resistor and I is the current through it. (check all that apply)

Therefore, the statements 1 and 3 are true.

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The correct answer is 21 m.

The term "uniformly accelerated motion" refers to a body or object moving at a consistent rate of acceleration. The absence of velocity does not imply constant acceleration. Therefore, if a body is in motion such that the amount of change in its velocity in equally spaced time intervals will be constant, then that is what is meant by uniform acceleration or uniform acceleration definition.

Given initial velocity = 0 m/s

acceleration = 6 m/s^2

The body's movement in nth seconds in terms of distance,

S_n = u + a/2 (2n-1)

S_4 = 0 + 6/2 ( 2 × 4 - 1 )

S_4 = 3 ( 8 -1 )

S_4 = 3 × 7

S_4 = 21 m

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The electric field at distance r from the axis where r < r . assume the charge density is positive  E = p× r / 2 ×e₀

Given:

- Volume of cylinder V = pi×r² ×L

- area A = 2× pi ×r ×L

- permittivity of space : e₀

Finding :

Electric field E at distance r from the axis, where r < R.

Solution:

Step 1: Application of Gauss Law

Form a Gaussian surface within the cylinder with r < R. Th cylinder has two surfaces i.e curved surfaces and end caps. thanks to long charge distribution the flux through is zero, since the surface dA of end cap and E are at 90 degree angle to at least one another; hence, E . dA = E× dA ×cos(90) = 0.

For the curved surface we have:  

                 (surface integral) E.dA = Q_enclosed / e₀

Step 2: The charge enclosed (Q_enclosed) is function of r and proportional density:

                   Q_enclosed = p ×V

                                   Q_enclosed = p ×pi ×r² ×L

Step 3: the world of the curved surface:

                                  dA = 2× pi ×r ×L

Step 4: Computing E:

                         E×(2 ×pi ×r ×L) = p× pi ×r^2×  L / e₀

                                 E = p×r / 2×e₀

The charge density is that the measure of electric charge per unit area of a surface, or per unit volume of a body or field. The charge density tells us what proportion charge is stored in a particular field. Charge density are often determined in terms of volume, area, or length.

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The attitudes and expectations around gender roles are often founded on gender stereotypes, or oversimplified ideas about the attitudes, attributes, and behavior patterns of males and females, rather than on any inherent or natural gender distinctions.

Gender stereotypes are broadly accepted ideas about traits that are considered suitable for males and females. There really are gender stereotypes regarding character, profession, and skills. These prejudices are reflected in gender roles, which are commonplace actions.

Hence Understanding these beliefs and their origins is essential to conquering them even if they are typically damaging to society.

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