(a). A particle, whose acceleration is constant, is moving in the negative x direction at a speed of 4.36 m/s, and 10.9 s later the particle is moving in the positive x direction at a speed of 7.94 m/s. Find the acceleration?(b). what will be the velocity 10.9 second before it was moving in the negative x directionat the speed of 4.36 m/s(c). when is the particle at rest. express this answer as a time in seconds elapsed since it was moving in the negative x-direction at a speed of 4.36 m/s.

Complete question is;

Assuming 100% efficient energy conversion how much water stored behind a 50 centimeter high hydroelectric dam would be required to charge the battery with power rating, 12 V, 50 Ampere-minutes

Answer:

Amount of water required to charge the battery = 7.35 m³

Explanation:

The formula for Potential energy of the water at that height = mgh

Where;

m = mass of the water

g = acceleration due to gravity = 9.8 m/s²

H = height of water = 50 cm = 0.5 m

We know that in density, m = ρV

Where;

ρ = density of water = 1000 kg/m³

V = volume of water

So, potential energy is now given as;

Potential energy = ρVgH = 1000 × V × 9.8 × 0.5 = (4900V) J

Now, formula for energy of the battery is given as;

E = qV

We are given;

q = 50 A.min = 50 × 60 = 3,000 C

V = 12 V

Thus;

qV = 3,000 × 12 = 36,000 J

E = 36,000 J

At a 100% conversion rate, the energy of the water totally powers the battery.

Thus;

(4900V) = (36,000)

4900V = 36,000

V = 36,000/4900

V = 7.35 m³

The polynomial relationship between position and time for the bowling ball is linear.

A linear relationship between two variables is a term used to describe a straight-line relationship between the two variables.

Linear relationships can be expressed either in a graphical format or as a mathematical equation of the form y = mx + b.

From the equation of linear relationship between two variable, the highest power of x is one.

The given equation for position and time;

x(t) = vot + xo

From this given equation, the highest power of t is one, hence it is called linear relationship.

Thus, the polynomial relationship between position and time for the bowling ball is linear.

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Answer:

The maximum reaction time is approximately 13 seconds

Explanation:

In order to answer this problem let's start by converting the speed of the ranger's vehicle from miles per hour into feet per second, knowing that 1 mile is the same as 5280 ft and i hour is 3600 seconds:

\(11.8\, \frac{mi}{h} =11.8 \,\frac{5280\,ft}{3600\,s} \approx 17.3\,\frac{ft}{s}\)

Now, with this information, we set the equation for the amount of time needed to reduce the speed from 17.3 ft/s to full stop (0 ft/s):

\(v_f-v_i=-9.18 \,t\\0-17.3=-9.18\,t\\t=\frac{17.3}{9.18} \,s\\t\approx 1.88\,s\)

Now, the space covered during these 1.88 s when the vehicle reaches full stop while it decelerates is calculated via:

\(x_f-x_i=v_i\,t + \frac{1}{2} a\,t^2\\x_f-x_i=17.3\,t-\frac{9.18}{2} \,t^2\\x_f-x_i=17.3\,(1.88)-4.59\,(1.88)^2\\x_f-x_i=16.3\,ft\)

So, the maximum amount of time the ranger has to react and press the break while driving at 17.3 ft/s is the time to cover 242 ft minus 16.3 ft = 225.7 ft

During 225.7 ft the ranger could be driving in uniform motion (with speed 17.3 ft per second), we find the time to cover such:

\(x_f-x_i=v_i\,t\\225.7 = 17.3\,t\\t= \frac{225.7}{17.3} \\t\approx 13\, seconds\)

Answer: Hope this helps!!!!

Explanation:

The answer is true, that the hydraulic press utilizes Bernoulli's principle.

It can be derived from the Principle of conservation of energy.

According to Bernoulli's principle, which governs fluid dynamics, a fluid's speed increases concurrently with a reduction in pressure or potential energy. The mathematical concept is named after Swiss mathematician Daniel Bernoulli, who first published it in his book Hydrodynamics in 1738.

The venturi tube is a real-world example of Bernoulli's Principle in action. The venturi tube has an air intake that constricts to a throat and an exit segment that widens as it moves backward. The entrance and outflow both have the same diameter.

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The large ball, small ball, and feather fall to Earth and do not move towards each other due to the force of gravity, which is proportional to the mass of the objects involved and inversely proportional to the square of the distance between them. Earth's gravitational force is much stronger than the gravitational force between the objects, leading to their downward motion.

The reason the large ball, small ball, and feather fall to Earth and do not move towards each other is due to the force of gravity. Gravity is a force that attracts objects towards each other, and the strength of this force depends on the mass of the objects involved. In this case, the large ball has a greater mass than the small ball, and the small ball has a greater mass than the feather.

According to Newton's law of universal gravitation, the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. Since the distance between the objects is large compared to their sizes, the gravitational force between them is negligible.

Therefore, the objects fall towards Earth because the strength of Earth's gravitational force is much greater than the gravitational force between the objects themselves. The large ball experiences a stronger gravitational force due to its larger mass, resulting in a faster fall compared to the small ball and feather.

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a) The value of t u = 140/t`b.

b) The y position of the cannonball at the time t is  55.5 mc.

c) The initial speed of the projectile is 52.4 m/s.

Given that a cannonball is fired horizontally from the top of a cliff. The cannon is at height H = 55.5 m above ground level, and the ball is fired with initial horizontal speed u. The projectile lands at a distance D = 140 m from the cliff. Assume that the cannon is fired at time t = 0 and that the cannonball hits the ground at time t.Now,We have to find the value of t, y position of the cannonball at the time t and the initial speed of the projectile.

a. To find the value of t:Here, we have to use the formula of distance

i.e.,S = ut + (1/2)gt², Where S = 140 m, u = u and g = 9.8 m/s².Hence,140 = u×t ………..(1)We know that, time taken by the cannonball to hit the ground can be calculated as,`(2H)/g`

Since the height of the cannon from the ground is 55.5m, the total height of the cannonball from the ground is

(2H) = 2 × 55.5

= 111 m`2H/g

= 111/9.8`

= 11.32653 s

From equation (1),u×t = 140u = 140/t

Therefore, `u = 140/t`b.

b)To find the y position of the cannonball at the time t:

Here, we have to use the formula of height i.e.,y = u×t – (1/2)gt²,

Where, y = height of the cannonball at time t, u = 140/t, t = time taken by the cannonball to hit the ground and g = 9.8 m/s².

We have already calculated the time taken by the cannonball to hit the ground in the previous step.`

y = 140 - (1/2) × 9.8 × t²`

On substituting the value of t as `t = 11.32653`,

we get,y = 140 - (1/2) × 9.8 × (11.32653)²= 55.5 mc.

c)  To find the initial speed of the projectile:

To calculate the initial speed of the projectile, we need to use the formula of range of projectile

.i.e.,R = u²sin2θ/g

Where R = 140 m, g = 9.8 m/s², θ = 0° (horizontal)

u² = R × g/sin2θ

   = 140 × 9.8/sin0°  

   = 2744m²/s²u  

   = \(\sqrt(2744m^2/s^2)\)

   = 52.4 m/s

Hence, the initial speed of the projectile is 52.4 m/s.

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The current sensitivity of a moving coil galvanometer increases with a decrease in its resistance.

What is Current Sensitivity?

Current sensitivity is a measure of the responsiveness of an instrument to the current flowing through it. In particular, it is the deflection produced by a given amount of current passing through a device. The higher the current sensitivity, the smaller the amount of current required to produce a given deflection, and thus the more sensitive the instrument is to changes in current.

This is because the current sensitivity of a galvanometer is defined as the deflection produced per unit of current passed through it. Therefore, a higher current sensitivity means that a smaller current can produce a larger deflection, which can be achieved by decreasing the resistance of the galvanometer. This is because a lower resistance will allow a larger current to flow through the coil, which will result in a larger deflection of the coil.

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Answer:

Resistance

Explanation:

Sensitivity of a moving coil galvanometer can be increased by increasing the number of turns in the coil, the area of coil and magnetic field whereas by decreasing the couple per unit twist of the suspension.

The half-life of hypothetical element  technetium-99 is 210,936 years.

Half-life of the hypothetical element From the graph provided in the question, the half-life of the hypothetical element can be obtained by finding the time taken for the element to reduce to half its original quantity. Here, it can be seen from the graph that the quantity of the element reduces from 40 to 20 on day 4. Therefore, the half-life of the hypothetical element is 4 days.2. Time taken for a sample to decay from 100 grams to 25 gramsIf the half-life of a given substance is 65 days, then the quantity of the substance reduces to half every 65 days. From 100 grams to 50 grams, it takes one half-life cycle. From 50 grams to 25 grams, it will take another half-life cycle.

Therefore, it will take two half-life cycles, which is 2 × 65 = 130 days, for a 100-gram sample of the substance to decay until there is only 25 grams of the radioactive material remaining.3. Half-life of a sample that decays from 200 grams to 50 grams in 60 minutesIt is given that the sample of radioactive isotopes takes 60 minutes to decay from 200 grams to 50 grams. To find the half-life, we need to determine how many times the sample has lost half of its mass, which tells you how many half-life cycles have occurred.At 30 minutes, the sample reduces to half its original quantity, which is 100 grams. At 45 minutes, it reduces to 50 grams, which is half of 100 grams. Therefore, it takes two half-life cycles to reduce from 200 grams to 50 grams in 60 minutes. Hence, the half-life of the isotope is 15 minutes.4. Half-life of technetium-99 that decays from 500.0 g to 62.5 g in 639,000 yearsIt is given that a 500.0 g sample of technetium-99 decays to 62.5 g of technetium-99 remaining in 639,000 years. We can use the half-life formula to find the half-life of technetium-99.t1/2 = (t × log2) / log(N0 / Nt) Where,t1/2 = half-life of the substanceN0 = initial quantity of the substance Nt = quantity of the substance left after time t (in years)t = time (in years)From the given data,t1/2 = (639000 × log2) / log(500.0 / 62.5)t1/2 = 210,936 years.

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Answer: C.

Correct me if I'm wrong.

Answer:

The graph of the velocity of an object in free fall would look like a straight line sloping downward. As the object falls, its velocity increases at a constant rate, so the graph of its velocity versus time will be a straight line with a negative slope. This is because acceleration due to gravity is a constant -9.8 meters per second squared, so the velocity of a free-falling object will increase by 9.8 meters per second every second.

Therefore, the graph that shows the change in velocity of an object in free fall is a straight line with a negative slope. Here is an example of such a graph:

Free Fall Velocity Graph

The answer is option C) The car experienced negative acceleration with velocity in the positive direction.

During the nuclear change we can expect to see different chemical symbols before and after the change

Chemical and nuclear reactions are quite different from one another. Atoms can share electrons with other atoms or participate in an electron transfer to increase their stability in chemical reactions. In nuclear reactions, the atom's nucleus stabilizes itself by going through some sort of alteration. Compared to the energies involved in chemical reactions, the energies produced in nuclear reactions are many orders of magnitude higher. Environmental factors like temperature or pressure do not significantly affect nuclear reactions like they do with chemical ones.

Nuclear reactions involve a change in an atom's nucleus, usually producing a different element. Chemical reactions, on the other hand, involve only a rearrangement of electrons and do not involve changes in the nuclei

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Answer:

Earth-crossing asteroid, asteroid whose path around the Sun crosses Earth's orbit. Two groups of such asteroids—Aten and Apollo asteroids—are distinguished by the size of their orbits and how closely they approach the Sun.

Explanation:

The coefficient of kinetic friction between the block and the rough surface is -0.6.

Kinetic friction is a type of friction that occurs when two objects are in contact and moving relative to each other. It is also known as sliding friction or dynamic friction. Kinetic friction is caused by the interaction of the two surfaces as they move against each other. The force of kinetic friction acts in the opposite direction of the motion of the two objects and is proportional to the normal force between them. The coefficient of kinetic friction is a measure of the amount of friction between two surfaces and is determined by the materials of the two surfaces.

The coefficient of kinetic friction can be found using the equation:
μk = (vf - vi) / (d * a)
where μk is the coefficient of kinetic friction, vf is the final velocity, vi is the initial velocity, d is the distance traveled, and a is the acceleration due to gravity (9.8 m/s2).
Plugging in the given values, we get:
μk = (6 - 18) / (30 * 9.8)
μk = -0.6
Therefore, the coefficient of kinetic friction between the block and the rough surface is -0.6.

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Answer:

5m

Explanation:

\(4^{2}+3^{2}=5^{2}\\5^{2}=25\)

Use the Pythagorean theorem to calculate the long edge of the triangle, which would be his displacement.

Answer:

Explanation:

The kinetic energy of an object can be found by using the formula

\(k = \frac{1}{2} m {v}^{2} \\ \)

m is the mass

v is the velocity

From the question we have

\(k = \frac{1}{2} \times 8 \times {4}^{2} \\ = 4 \times 16\)

We have the final answer as

Hope this helps you

the answer to your question is 200 J

Answer:

Explanation:

Scientific laws or laws of science are statements, based on repeated experiments or observations, that describe or predict a range of natural phenomena.

Diamond, graphite and fullerenes (substances that include nanotubes and 'buckyballs' , such as buckminsterfullerene) are three allotropes of pure carbon. In all three allotropes, the carbon atoms are joined by strong covalent bonds, but in such different arrangements that the properties of the allotropes are very different.

Because of their distinctive structural makeup, graphite and diamond are distinct materials. Both have extremely high melting points due to their giant covalent structures. Diamond is incredibly strong and hard due to the four covalent links that each carbon atom in the mineral has with other carbon atoms. However, because each carbon in graphite is connected to three other carbons, it forms in layers.

Even though graphite is used to make pencils, despite the fact that each carbon atom only has three bonds, the layers are actually highly strong and have delocalized "free" electrons between them. Graphite appears soft because these electrons act as a lubricant between layers, allowing them to slide over one another. Graphite conducts electricity due to the free electrons. Diamond does not carry electricity because it lacks these free electrons.

There are more than three allotropes of carbon. These include diamond, graphite, graphene, carbon nanotubes, fullerenes, and carbon nanobuds.

Diamond

In a three-dimensional array, four additional carbon atoms are covalently attached to each carbon atom in a diamond. In essence, a diamond is one enormous molecule.

Graphite

The carbon atoms in graphite are bonded together in sheets of connected hexagons that resemble chicken wire. In essence, each sheet is a single molecule.

Each carbon atom in a sheet establishes solid covalent bonds with three other carbon atoms. The only forces keeping the sheets packed together are the modest intramolecular forces.

Graphene

In the form of a single sheet of graphite that is only one atom thick, graphene is made up entirely of carbon.

Nanocarbon tubes

Graphene sheet wrapped into a cylindrical tube of carbon atoms is how a carbon nanotube looks. Each atom connected to three other atoms, and the tube is one atom thick.

C60 and buckminsterfullerene

A single sheet of carbon atoms that has been folded into a spherical is what makes up buckminsterfullerene. Three additional atoms are connected to each carbon atom. With a carbon atom at each of the 20 hexagonal and 12 pentagonal corners, sixty carbon atoms are arranged in the shape of a ball.

There are numerous other known carbon balls, such as C70, C76, C84, and C540. They are collectively referred to as "buckyballs" or "fullerenes" and have varying amounts of pentagons and hexagons.

Nanocarbon buds

An allotrope of carbon called carbon nanobuds has fullerene-like "buds" that are covalently bonded to the sidewalls of carbon nanotubes.

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For a given length of the pendulum and acceleration of the cart, the maximum displacement angle can be determined using the above formulas.

What is Acceleration?

Acceleration can be positive or negative depending on the direction of the change in velocity. If an object is speeding up, the acceleration is positive, while if it is slowing down, the acceleration is negative.

(1) The maximum displacement angle observed in a pendulum experiment can be determined by the length of the pendulum and the acceleration due to gravity. According to the theory of simple harmonic motion, the period of a pendulum is directly proportional to the square root of its length and inversely proportional to the square root of the acceleration due to gravity.

The formula for the period of a pendulum is:

T = 2π * sqrt(L/g)

where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity (approximately 9.8 m/\(s^{2}\)).

For a given length of the pendulum, the maximum displacement angle occurs when the pendulum is at the highest point in its swing (i.e., when its velocity is momentarily zero). At this point, all of the energy of the pendulum is potential energy (i.e., gravitational potential energy), and the angle is known as the maximum displacement angle or the amplitude.

The maximum displacement angle (θ) can be calculated using the formula:

θ = \(sin^{^-1(a/g)}\)

where a is the acceleration of the cart.

Therefore, for a given length of the pendulum and acceleration of the cart, the maximum displacement angle can be determined using the above formulas.

(2) If the rod is hung 8 cm from its endpoint instead of 28 cm, the length of the pendulum (L) would be 20 cm. Using the same formula as above, the period of the pendulum would be:

T = 2π * sqrt(0.2/9.8) = 0.898 seconds

The maximum displacement angle can be calculated using the same formula as above:

θ = sin^\(sin^{^-1(a/g)}\)

where a is the acceleration of the cart.

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This is a uniform rectilinear motion (MRU) exercise.

To start solving this exercise, we obtain the following data:

To calculate distance, speed is multiplied by time.

We apply the following formula: d = v * t.

We substitute the data in the formula: the speed is equal to 4.6 m/s, the time is equal to 10 s, which is left as follows:

\(\bf{d=4.6\dfrac{m}{\not{s}}*10\not{s} }\)

\(\bf{d=46 \ m}\)

Therefore, the speed at 10 seconds is 46 meters.

\(\huge \red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}\)

The rock hit the man with a power equal to 588.6 W.

The power can be described as the rate of doing work and is measured in SI units of joules per second (J/s) or Watt (W). Power can be defined as a time-based quantity.

The mathematical expression of the power can be represented as:

Power = Work/time

P = W/t

Given, the mass of the rock, m = 15 kg

The gravitational acceleration of the rock, g = 9.81 m/s²

The work needed to fall rock from a given height, W = mgh

W = 15 × 9.81 × 10

W = 1.47 ×10³ J

The time is taken by a rock to fall, t = 2.5 s

The power with which it hit the man, P = W/t

P =  1.47 ×10³/2.5

P = 588.6 W

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Change in velocity, \(\Delta v\), is the initial velocity subtracted from the final velocity. \(\Delta v = v_{2} - v_{1} = 35 - 20 = 15kmh^{-1}\)

The change in the velocity of Maria's car is equal to 15 Km/h.

Velocity can be defined as a vector measurement of the rate of motion and direction of an object. The velocity of an object can be defined as the rate of change in the position of the body with respect to time.

Velocity can be defined as a vector parameter as it exhibits both magnitude and direction. A mathematical formula to calculate the velocity of the object can be represented as:

v = d / t

Where v is the velocity of the object, d is the distance, and t is the time taken by the object.

Although the S.I. unit for the measurement of the velocity is m/s and can also expressed in the terms of miles per hour (mph), and kilometers per hour(kph).

Given, the initial velocity of Maria's car, v₁ = 20 m/s

The final velocity of Maria's car, v₂ = 35 m/s

The change in the velocity of Maria's car, Δv = v₂ - v

Δv = = 35 - 20

Δv = 15 km/h

Therefore, the change in velocity is 15 Km/h.

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He was solely consuming high-fat foods until recently, when he began consuming nutritious foods.

Briefing:

Instead of helping you lose weight, hopping from one diet fad to another can make you put on weight. Your daily calorie intake can fluctuate significantly, which can cause your metabolism to slow down. To adjust to new food, your metabolism needs about three weeks.

Obesity is typically brought on by excessive eating and insufficient exercise. A large portion of the excess energy will be stored by the body as fat if you consume large amounts of energy, especially fat and sugars, without expelling it through exercise and physical activity.

Even if the food is good for you, the calories can still add up and result in a weight loss plateau or even weight gain.

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The force needed to accelerate a mass of 40 kg from velocity v₁ = (4î - 5) + 3k)m/s to v = (8î + 3) - 5k)m/s in 10 seconds is 12.4 N.

Start by calculating the change in velocity (Δv) experienced by the object. This can be done by subtracting the initial velocity v₁ from the final velocity v.

Δv = v - v₁ = ((8î + 3) - 5k) - ((4î - 5) + 3k)

= 8î + 3 - 5k - 4î + 5 - 3k

= 4î - 8k + 8

Next, calculate the acceleration (a) using the formula:

a = Δv / t

where t is the time interval, given as 10 seconds.

a = (4î - 8k + 8) / 10

= (0.4î - 0.8k + 0.8) m/s²

The force (F) required to accelerate the object can be found using Newton's second law:

F = m * a

where m is the mass, given as 40 kg.

F = (40 kg) * (0.4î - 0.8k + 0.8) m/s²

= (16î - 32k + 32) N

Simplify the expression to obtain the final answer:

F = 16î - 32k + 32 N

≈ 12.4 N

Therefore, the force needed to accelerate a mass of 40 kg from velocity v₁ = (4î - 5) + 3k)m/s to v = (8î + 3) - 5k)m/s in 10 seconds is approximately 12.4 N.

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(a) The ball goes up to the height of 31.89 m. (b) The ball stays for 5.1 s in the air. (c) The acceleration due to gravity and wind resistance can affect the estimation.

Acceleration owing to gravity is the term used to describe the rate at which a body's velocity changes as a result of the earth's gravitational pull. In general, it is assumed that the acceleration caused by gravity is in the downward direction.

The acceleration caused by gravity has been calculated as, however as it changes from location to location, it may have an impact on the estimation.

You may have thought that the wind has no impact, but it can actually generate drag and even cause the ball to shift course.

Therefore, (a) The ball goes up to the height of 31.89 m. (b) The ball stays for 5.1 s in the air. (c) The acceleration due to gravity and wind resistance can affect the estimation.

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Explanation:

The ideal gas law can be used to calculate the pressure of a gas at a given temperature and volume. The ideal gas law is given by the equation PV = nRT, where P is the pressure of the gas, V is the volume of the gas, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature of the gas.

To solve this problem, we need to first convert the temperature in degrees Celsius to degrees Kelvin. This is because the ideal gas constant has units of energy per mole per Kelvin, and the temperature in the ideal gas law must be in Kelvin. To convert from degrees Celsius to degrees Kelvin, we simply add 273.15 to the temperature in degrees Celsius. Therefore, the temperature of the gas in Kelvin is -3 + 273.15 = 270.15 K.

Next, we need to know the volume of the gas in the container. If the container is rigid, then the volume of the gas will not change, regardless of the temperature of the gas. Therefore, we can assume that the volume of the gas is the same at both temperatures. We can also assume that the number of moles of gas in the container remains constant, since the container is sealed and no gas can escape or enter the container.

With this information, we can plug the values into the ideal gas law equation and solve for the pressure at the higher temperature:

PV = nRT

P = (nRT) / V

P = (n * 8.314 * 270.15) / V

P = (n * 8.314 * 267) / V

We know the value of V, the volume of the gas, and the value of n, the number of moles of gas, but these values are not given in the problem. Therefore, we cannot solve for the pressure of the gas at the higher temperature without knowing these values.

The arrows are drawn in the figure which shows gravitational forces on each person on earth.

Gravitational force is force of attraction between two masses. Gravitational force(F) between two bodies is directly proportion to the product of masses(m₁,m₂) of two bodies and inversely proportional to square of distance(r) between them. mathematically it is written as,

F∝ m₁.m₂

F ∝ 1/r²

F = G m₁,m₂÷r²

where G is gravitational constant, whose value is 6.6743 × 10⁻¹¹ m³ kg-1s⁻².

Force is expressed in Newton N in SI unit. its dimensions are [M¹L¹T⁻²].

This is analogous with coulomb's law which gives force between two charges.

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