What are unit of g. Derive an expression for it. *
Answers
Answer:
Gravitational Constant. In SI units, G has the value 6.67 × 10-11 Newtons kg-2 m2. The direction of the force is in a straight line between the two bodies and is attractive. Thus, an apple falls from a tree because it feels the gravitational force of the Earth and is therefore subject to “gravity”.
Explanation:
What is Acceleration due to Gravity?
Acceleration due to gravity is the acceleration gained by an object due to gravitational force. Its SI unit is m/s2. It has both magnitude and direction, hence, it’s a vector quantity. Acceleration due to gravity is represented by g. The standard value of g on the surface of the earth at sea level is 9.8 m/s2.
Acceleration due to Gravity – Formula, Unit and Values
Acceleration Due to Gravity (g)
Symbol g
Dimensional Formula M0L1T-2
SI Unit ms-2
Formula g = GM/r2
Values of g in SI 9.806 ms-2
Values of g in CGS 980 cm s-2
Table of Content:
What is Gravity?
Formula
g on Earth
Value of g with Height
g with Depth
g due to Shape of Earth
g due to Rotation
What is Gravity?
Gravity is the force with which earth attracts a body towards its centre. Let us consider two bodies of masses ma and mb. Under the application of equal forces on two bodies, the mass in terms of mass is given by:
mb = ma [aA/aB] this is called an inertial mass of a body.
Under the gravitational influence on two bodies, the mass in terms of mass is given by,
FA = GMmA/r2,
FB = GMmB/r2,
mB = [FB/FA] × mA
⇒ More on Gravitation:
Newton’s Law of Gravitation
Gravitational Potential Energy
Gravitational Field Intensity
The above mass is called a gravitational mass of a body. According to the principle of equivalence, the inertial mass and gravitational mass are identical. We will be using this while deriving acceleration due to gravity given below.
Let us suppose a body [test mass (m)] is dropped from a height ‘h’ above the surface of the earth [source mass (M)], it begins to move downwards with an increase in velocity as it reaches close to the earth surface.
We know that velocity of an object changes only under the action of a force, in this case, the force is provided by the gravity.
Under the action of gravitational force, the body begins to accelerate toward the earth’s centre which is at a distance ‘r’ from the test mass.
Then, ma = GMm/r2 (Applying principle of equivalence)
⇒ a = GM/r2 . . . . . . . (1)
The above acceleration is due to the gravitational pull of earth so we call it acceleration due to gravity, it does not depend upon the test mass. Its value near the surface of the earth is 9.8 ms-2.
Therefore, the acceleration due to gravity (g) is given by = GM/r
Formula of Acceleration due to Gravity
Force acting on a body due to gravity is given by, f = mg
Where f is the force acting on the body, g is the acceleration due to gravity, m is mass of the body.
According to the universal law of gravitation, f = GmM/(r+h)2
Where,
f = force between two bodies,
G = universal gravitational constant (6.67×10-11 Nm2/kg2)
m = mass of the object,
M = mass of the earth,
r = radius of the earth.
h = height at which the body is from the surface of the earth.
As the height (h) is negligibly small compared to the radius of the earth we re-frame the equation as follows,
f = GmM/r2
Now equating both the expressions,
mg = GmM/r2
⇒ g = GM/r2
Therefore, the formula of acceleration due to gravity is given by, g = GM/r2
Note: It depends on the mass and radius of the earth.
This helps us understand the following:
All bodies experience the same acceleration due to gravity, irrespective of its mass.
Its value on earth depends upon the mass of the earth and not the mass of the object.
Acceleration due to Gravity on the Surface of Earth
Earth as assumed to be a uniform solid sphere with a mean density. We know that,
Density = mass/volume
Then, ρ = M/[4/3 πR3]
⇒ M = ρ × [4/3 πR3]
We know that, g = GM/R2.
On substituting the values of M we get,
g = 4/3 [πρRG]
At any distance ‘r’ from the centre of the earth
g = 4/3 [πρRG]
The value of acceleration due to gravity ‘g’ is affected by
Altitude above the earth’s surface.
Depth below the earth’s surface.
The shape of the earth.
Rotational motion of the earth.
Answer:
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