show that f(v)dv = 1 ,where f(v) is the maxwell boltzmann distribution equation​

The gravitational acceleration of a planet is proportional to the planet's mass, and inversely proportional to square of the planet's radius.

So when you stand on the surface of this particular planet, you feel a force of gravity that is

(1/2) / (3²)

of the force that you feel on the surface of the Earth.

That's (1/18) as much as on Earth.

The acceleration of gravity there would be about 0.545 m/s².  

This is about 12% less than the gravity on Pluto.

Explanation:

m = 4kg

u = 20m/s

t = 10s

v = 60m/s

initial momentum = mass × initial velocity

= 4 × 20 = 80kgm/s

⇒ Acids taste sour, react with metals, react with carbonates, and turn blue litmus paper red. Bases taste bitter, feel slippery, do not react with carbonates and turn red litmus paper blue.

The study of acids and bases is crucial to chemistry. The Lewis acid/base motif, which broadens the concept of an acid and base beyond H+ and OH- ions, is one of the most relevant theories.

Acids are ionic compounds, which means they have a positive or negative charge. In water, these ionic compounds separate to create hydrogen ions, or H+.

The quantity of H+ ions in the solution determines how strong an acid is. Acid is stronger the more H+ there is. Bases are ionic substances that separate in water to produce the negatively charged hydroxide ion (OH-). The quantity of Hydroxide ions in a base determines its strength (OH-). The strength of the base increases with OH- ion concentration.

Hope this helps,

- Eddie.

Answer:Materials that absorb light are called pigments. Pigments are colored substances that absorb certain wavelengths of light and reflect others. For example, a red pigment absorbs all colors of light except red, which it reflects. Materials that reflect light are called reflective materials. Reflective materials are materials that reflect light instead of absorbing it. Examples of reflective materials include aluminum foil and mirrors. Some materials, such as glass, are transparent and allow light to pass through them

Each of the five friends needs to pay £12 to cover the cost of their own meals and contribute towards the birthday person's meal. Using mean allows us to distribute the cost equally among the friends, ensuring a fair division of expenses for the meal.

To determine how much each of the five friends needs to pay, we can use the concept of averages (mean) and divide the total cost by the number of people paying.

In this scenario, the total cost of the meal for 6 people is £12 per person. Since the other 5 friends have decided to pay for the birthday person's meal, they will collectively cover the cost of their own meals plus the birthday person's meal.

To calculate the total cost covered by the five friends, we can subtract the cost of one person's meal (since the birthday person's meal is being paid by the group) from the total cost. The cost of one person's meal is £12.

Total cost covered by the five friends = Total cost - Cost of one person's meal

= (£12 x 6) - £12

= £72 - £12

= £60

Now, to find out how much each of the five friends needs to pay, we divide the total cost covered by the five friends (£60) by the number of friends (5).

Amount each friend needs to pay = Total cost covered by the five friends / Number of friends

= £60 / 5

= £12

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The temperature would rise by 1.8 degrees Fahrenheit if it went from 20 to 21 degrees Celsius.

Since 1880, the Earth's temperature has increased by an average of 0.14° F (0.08° C) per decade, or nearly 2° F overall. Since 1981, the pace of warming has increased more than double, to 0.32° F (0.18° C) every decade.

To assist us remember that as we move up the scale, we go from colder to hotter, let's label our thermometer. In other terms, a higher number of Fahrenheit degrees is hotter than a lower number of Fahrenheit degrees.

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The potential energy is at the maximum when you reach the top of your jump on a trampoline. The correct answer is option B.

Potential Energy is the type of energy an object possesses by virtue of its position relative to others, stresses within itself, electric charge, and other factors. Potential energy exists in various forms, including gravitational potential energy, elastic potential energy, chemical potential energy, and electrical potential energy.

This type of energy can be converted into another type of energies. Examples, a charged battery has potential energy and it can be used as electrical potential energy. Petrol, diesel and and gas have chemical potential energy and be used as kinetic energy.

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The right sphere will acquire an equal and opposite net positive charge to balance the negative charge on the left sphere.

Since the left sphere is attracted to the positively charged rod, it means that the left sphere acquires a temporary negative charge due to induction.

The positive charge on the rod repels electrons in the left sphere, causing them to move away from the rod side and accumulate on the opposite side, resulting in a net negative charge on the left sphere.

According to the principle of charge conservation, the net charge on the system must remain zero. Therefore, the right sphere acquires an equal and opposite net positive charge to balance the negative charge on the left sphere.

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Answer: C

C. Place plastic around the metal wires, because electric charges

hardly move in plastic.

Answer:

C is the correct answer

Explanation:

the two springs are each compressed by 25 cmcm when the cars are instantaneously at rest, just before they rebound id 13020 N/m.

Speed is the rate at which somebody is traveling.

From energy conservationists at the instant just before rebounds all the kinetic energy of cars will be transferred in the form of spring potentially energy then,

Total kinetic energy = maximum spring potential

0.5*m1*v1^2 + 0.5*m2*v2^2 = n*(0.5*k*x^2)

here, m1 = mass of car 1 = 250 kg

v1 = speed of car1 = 1.5 m/s

m2 = mass of car 2 = 150 kg

v2 = speed of car 2 = 2.5 m/s

n = number of spring = 2

k = spring constant = ??

x = change in length of each spring = 24.0 cm = 0.24 m

then,

0.5*250*1.5^2 + 0.5*150*2.5^2 = 2*0.5*k*(0.24^2)

k = (0.5*250*1.5^2 + 0.5*150*2.5^2)/(0.24^2)

k = 13020 N/m

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Answer:

acceleration = change in velocity / change in time

acceleration = 14/10

acceleration = 1.4/s^2

Answer:

Explanation:

Given

  mass A = 2.0 kg

  mass B = 3.0 kg

  θ = 40°

Find

  The tension in the string

  The acceleration of the masses

Solution

Mass A is being pulled down the inclined plane by a force due to gravity of ...

  F = mg·sin(θ) = (2 kg)(9.8 m/s^2)(0.642788) = 12.5986 N

Mass B is being pulled downward by gravity with a force of ...

  F = mg = (3 kg)(9.8 m/s^2) = 29.4 N

The tension in the string, T, is such that the net force on each mass results in the same acceleration:

  F/m = a = F/m

  (T -12.59806 N)/(2 kg) = (29.4 N -T) N/(3 kg)

  T = (2(29.4) +3(12.5986))/5 = 19.3192 N

__

Then the acceleration of B is ...

  a = F/m = (29.4 -19.3192) N/(3 kg) = 3.36027 m/s^2

The string tension is about 19.3 N; the acceleration of the masses is about 3.36 m/s^2.

Explanation:

If your reaction time is 1 second, then the new reaction time for each is:

Alcohol: 0.30 × 1 + 1 = 1.30

Drugs: 0.50 × 1 + 1 = 1.50

Cell phone: 0.20 × 1 + 1 = 1.20

The force on each side of the loop is 5.1 × 10^-5 N in the direction perpendicular to the wire and the magnetic field, and the direction of the force is determined by the right-hand rule.

The force on each side of the loop can be calculated using the formula F = BIL, where F is the force, B is the magnetic field, I is the current, and L is the length of the wire.

First, we need to find the magnetic field inside the solenoid. The magnetic field inside a solenoid is given by B = μ₀nI, where μ₀ is the permeability of free space, n is the number of turns per unit length, and I is the current.

In this case, the magnetic field inside the solenoid is B = μ₀nI = (4π × 10^-7 T·m/A)(25 turns/cm)(17.0 A) = 0.017 T.

Since the loop is perpendicular to the magnetic field, the angle between the current and the magnetic field is 90 degrees, and the force on each side of the loop is given by F = BIL. The length of each side of the square loop is L = 8.0 cm/4 = 2.0 cm.

Therefore, the force on each side of the loop is F = (0.017 T)(0.15 A)(2.0 cm) = 5.1 × 10^-5 N.

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Answer:

j

Explanation:

Answer:

a

Explanation:

The free body diagram of the squirrel motion, the weight of the squirrel is acting downwards while the air resistance is acting upwards.

The given parameters;

At a constant velocity downwards, the vertical acceleration is zero.

The downward force on the squirrel is calculated as follows;

W = mg - ma

W = m(g - a)

W = m(g - 0)

W = mg

W = 5 x 9.8

W = 49 N

The air resistance on the squirrel which is acting upwards is calculated as;

n = ma + mg

n = m(a + g)

n = m(0 + g)

n = mg

n = 5 x 9.8

n = 49 N

The free body diagram is presented below;

                                   ↑ n

                                   Ο

                                   ↓ W

Thus, in the free body diagram of the squirrel motion, the weight of the squirrel is acting downwards while the air resistance is acting upwards.

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Answer:

The correct option is A

Explanation:

For a substance to boil at 1415 °C shows the substance is an electrovalent/ionic substance (hence the elements are not the answer). Electrovalent/ionic substances are characterized by high melting and boiling points. Also, with a density of 3.13 g/cm³ (with a +/- 0.1 g/cm³), the correct answer is potassium iodide. This is because potassium iodide has a density of 3.12 g/cm³ (which is - 0.1 g/cm³). It should also be noted that pure potassium iodide boils at 1,330 °C, however the presence of impurities could increase the boiling point of the salt, thus an impure potassium iodide could have a density of 3.12 g/cm³ and a temperature around 1415 °C

"Potassium iodide" would it most likely be. A further explanation is provided below.

Given values are:

Density,

Boiling point,

Density can be change by,

Uncertainty in temperature,

We can take the value of density from:

We can take the value of temperature from:

After checking the ranges, we find "Potassium iodide" have density as well as temperature in our range.

Thus the above answer is right.

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The distance the ball was thrown is 52.22m by A quarterback throws a pass at an angle of 35° above the horizontal with an initial speed of 25 m/s. The ball is caught by the receiver 2.55 seconds later.

Every motion under constant acceleration is projectile motion

Angle above horizontal Ф = 35°, initial speed v1 = 25m/s , time 2.55s

Substituting value in the below equation

x=x₁ + (v₁*cosθ)(t)+1/2 *a*t²

a= 0 as acceleration in horizontal direction is zero

x= 25*cos(35)*2.55

x=52.22 m

Projectile motion is a form of motion in which object influenced when it is launched into the gravitational force from the surface of Earth along a curved path.

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The average acceleration of the motorcycle over the given distance is approximately 9.39 m/s².

To calculate the average acceleration of the motorcycle, we can use the formula:

Average acceleration = (final velocity - initial velocity) / time

First, let's convert the final velocity from km/h to m/s since the distance is given in meters. We know that 1 km/h is equal to 0.2778 m/s.

Converting the final velocity:

Final velocity = 78 km/h * 0.2778 m/s = 21.67 m/s

Since the motorcycle starts from rest (initial velocity is zero), the formula becomes:

Average acceleration = (21.67 m/s - 0 m/s) / time

To find the time taken to reach this velocity, we need to use the formula for average speed:

Average speed = total distance/time

Rearranging the formula:

time = total distance / average speed

Plugging in the values:

time = 50 m / 21.67 m/s ≈ 2.31 seconds

Now we can calculate the average acceleration:

Average acceleration = (21.67 m/s - 0 m/s) / 2.31 s ≈ 9.39 m/s²

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- The resistance of the first resistor (R₁) is 12 Ω.

- The electromotive force (EMF) of the battery is 18 V.

- The internal resistance of the battery is 12 Ω.

To solve the given problem, we can apply Kirchhoff's laws and Ohm's law to determine the resistance of the first resistor (R₁) and the electromotive force (EMF) and internal resistance of the battery.

Let's start by calculating the resistance of the first resistor (R₁):

1. Apply Ohm's law to find the voltage drop across the external circuit:

  V = I * R

  V = 1 A * 6 Ω

  V = 6 V

2. The voltage drop across the external circuit is equal to the EMF minus the voltage drop across the internal resistance of the battery:

  V = E - Ir

  6 V = E - (1 A * r)   (where r is the internal resistance of the battery)

3. We also know that the EMF of the battery is the sum of the voltage drops across each cell in the battery:

  E = 6 cells * 3 V/cell

  E = 18 V

4. Substitute the value of E in the equation from step 2:

  6 V = 18 V - r

  r = 12 Ω

Therefore, the resistance of the first resistor (R₁) is 12 Ω.

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Answer:

FALSE

Explanation:

The length of time that an action or state persists. The given L-shaped object made of two rods oscillates at a frequency of 2π√√2L/3g.

The rod weighs m grams.

The length of a single rod is L.

If it is connecting at, as indicated by the query, then the moment of inertia of the combined system follows.

mL²/3+3L²/3=2mL²/3

Here, I denotes the rod's moment of inertia, d denotes the separation of the center of gravity from the fixed point, and T denotes the length of time the L-shaped object oscillates.

Length of pendulam

Lcos45=L*1/√2=L/√2

Caluclate the time period

T=2π√I/mgl

=2π√2*mL²*√2/3*2mgl

oscillates at a frequency = 2π√√2L/3g

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Answer:

Explanation:

a)

The force on electron acts opposite to the velocity , and direction of force on electron is always opposite to direction of electric field .

Hence direction of electric field must be in the same  in which electrons travels.

Hence option iii is correct.

b )

deceleration a = force / mass

= qE / m

= 1.6 x 10⁻¹⁶ x 5.6 x 10⁵ / 9.1 x 10⁻³¹

= .98 x 10²⁰ m /s²

v² = u² - 2 a s

0 = (8.06 x 10⁶ )² - 2 x .98 x 10²⁰ s

s = 64.96 x 10¹² / 1.96 x 10²⁰

= 33.14 x 10⁻⁸ m

c ) time required

= 8.06 x 10⁶ / .98 x 10²⁰

= 8.22 x 10⁻¹² s .

d ) Its speed will be same as that in the beginning ie 8.06 x 10⁶ m/s .

Answer:

(a) Option (i)

(b) 6.6 x 10^-4 m  

(c) 8.2 x 10^-11 s

Explanation:

initial velocity, u = 8 .06 x 10^6 m/s

Electric field, E = 5.6 x 10^5 N/C

(a) The direction of field is opposite.

Option (i).

(b) Let the distance is s.  

Use third equation of motion

\(v^2 = u^2 + 2 a s \\\\0 = u^2 - 2 \times \frac{qE}{m}\times s\\\\8.06\times 10^6\times 8.06\times 10^6 = \frac {1.6\times 10^{-19}\times 5.6\times 10^5}{9.1\times 10^{-31}} s\\\\s = 6.6\times 10^{-4} m\)

(c) Let the time is t.

Use first equation of motion.

\(v = u + a t \\\\0 = u - \times \frac{qE}{m}\times t\\\\8.06\times 10^6 = \frac {1.6\times 10^{-19}\times 5.6\times 10^5}{9.1\times 10^{-31}} t\\\\t = 8.2\times 10^{-11} s\)

Answer:

act or process of measuring

Explanation:

Explanation:

the comparison of an unknown quantity with a known quantity.

Let F be the magnitude of the force needed to keep the box sliding at constant speed, and f the magnitude of kinetic friction. Then by Newton's second law, the net horizontal force on the crate is

F - f = 0

so that

F = f

f is proportional to the magnitude of the normal force n,

f = 0.38n

The net vertical force is

n - mg = 0

which tells us that

n = mg = (29 kg) (9.8 m/s²) ≈ 284 N

Then the required force must have magnitude

F = f = 0.38 (284 N) ≈ 110 N

A cell phone more likely to break when dropped from a higher height than a lower one because it has more potential energy at high height.

Potential energy is the energy stored by an object as a result of its position relative to other objects, internal tensions, electric charge, or other reasons.

Potential energy is commonly defined as an object's gravitational potential energy, the elastic potential energy of an extended spring, and the electric potential energy of an electric charge in an electric field. The joule is the SI unit of energy.

Although it has connections to the Greek philosopher Aristotle's concept of potentiality, the word potential energy was coined by the 19th-century Scottish engineer and physicist William Rankine.

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To determine the impulse we use the fact that the impulse is equal to the change in momentum:

Where:

The momentum is the product of the mass and the velocity, therefore, we have:

Since the initial velocity is zero, we have:

Now, we substitute the values:

Solving the operation:

Therefore, the momentum is 1607424 kgm/s

Due to the relationship between linear and angular speed, the candidate's speed is 13.3 m/s

A satellite orbiting the earth is one of the example of a circular motion. The satellite will experience gravitational attraction towards the center of the earth. This attraction force provides the centripetal force

Given that a prospective astronaut is spun around in a human centrifuge such that the candidate experiences a centripetal acceleration that is 2.5 times the acceleration due to gravity on the surface of the earth. If the candidate is 7.27 m from the center, the parameters to work on are

To determine the candidate's speed in meters per second, let us first find its angular speed w in rad/s by using the formula

a = w²r

24.5 = 7.27w²

w² = 24.5 / 7.27

w² = 3.37

w = √3.37

w = 1.84 rad/s

The relationship between linear and angular speed is

v = wr

v = 1.84 × 7.27

v = 13.3 m/s

Therefore, the candidate's speed in meters per second is 13.3 m/s

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