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Variation of Acceleration due to Gravity

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Overview

Weight of the body is high at poles than in equator. This note has brief information about difference in gravity within our earth and illustrates how falling rate or acceleration due to gravity is independent of the masses of the falling bodies.

Variation of Acceleration due to Gravity

Variation of 'g' on the poles & equator.

We know that the shape of the earth is not completely spherical rather it is oval as shown in the figure.

Due to this, the polar radius (Rp) of the earth is less than the equatorial radius (Re).

i.e. Rp < Re

Since acceleration due to gravity (g) is inversely proportional to the square of radius, the value of g is more at poles & less at equatorial region.

i.e.,gp > ge Because Rp< Re

Since gp > ge the weight of an object on poles is greater than on equator.

 

The weight of object at Solukhumbu and Janakpur:

The weight of the object is greater at Janakpur.

It is because weight of the body is directly proportional to acceleration due to gravity and acceleration due to gravity is inversely proportional to the radius plus height squared from sea level

i.e. w ∝ g and g ∝ \(\frac 1{(R + H)^2}\)

As Solukhumbu lies at the higher altitude than Janakpur, the value of g is less at Solukhumbu and accordingly the weight is less at Solukhumbu than Janakpur.

Feather and Coin experiment

Please watch below video for a demonstration of the experiment:

 

The main conclusion of feather and coin experiment is that the falling rate or acceleration due to gravity is independent of the masses of the falling bodies.

OR

If there is no air resistance than all the bodies fall together irrespective of their masses.

Fig 1.7 Coin and feather experiment

When a coin and a feather are freely falling in presence of air the air resistance experienced by each object is different as they have different size and structure. So they fall at different rate which is less than 9.8 m/s2. But in absence of air, there is nothing to resist their falling so they fall at the same rate 9.8 m/s2.

Things to remember
  • Acceleration due to gravity is high at poles than in equator.
  • Weight of the body is high at poles than in equator.
  • If there is no air resistance than all the bodies fall together irrespective of their masses.
  • It includes every relationship which established among the people.
  • There can be more than one community in a society. Community smaller than society.
  • It is a network of social relationships which cannot see or touched.
  • common interests and common objectives are not necessary for society.
Videos for Variation of Acceleration due to Gravity
Feather and Coin in a Vacuum
Your Weight Varies at Different Places On Earth
Questions and Answers
When a paratrooper is jumped from a great height, he falls down at the rate of acceleration due to gravity for a short time, after opening of parachute air exerts pressure in upward direction against the gravity. Thus, he lands safely on the ground.
The value of "g" is inversely proportional to the height from the earth surface.
i.e. where R is the radius of the earth and h is the height from the earth surface.
As the height in Terai is less than that in Himalayan region, "g" is greater in Terai region than the Himalayan region.
The three differences between acceleration due to gravity and gravitational constant are:
Gravity (g) Gravitational constant (G)
Its value is different at different places. Its value is constant which is equal to 6.67 × 10-11
Its unit is m/s2. Its unit is Nm2/kg2.
It is a vector quantity. It is a scalar quantity.

To lift any object, a force is needed and this force must exceed the weight of the object. As weight is calculated from mass of the object and acceleration due to gravity (m × g), a large object has a greater weight and a smaller object has a lesser weight. That's why it is difficult to lift a large stone on the surface of the earth but easy to lift small one.

The earth is not perfectly spherical but it is flattened at the poles and bulging out at the equator i.e. the radius of the equator is longer than the radius of the pole. As the "g" is inversely proportional to the square of the radius of the earth i.e., the value of "g" is more at the poles than at the equator.
Both the iron ball and feather will strike the ground at the same time in vacuum because the acceleration due to gravity is acting equally on all bodies irrespective of their mass due to the absence of air resistance.
On the surface of the moon the acceleration due to gravity on both the feather and the coin is the same. As there is no air (atmosphere) to give any resistance to them. Because of this, a feather and a coin fall simultaneously on the surface of the moon.
Acceleration due to gravity is produced on the freely falling body. The force is increased on the body because of acceleration due to gravity. Therefore, there is more probability of getting hurt when a man jumps from a significant height.

We have,
Mass of the moon (M)= 7.2 × 1022 kg
Radius of the moon (R) = 1.7 × 106 m
Mass of a man (m) = 60 kg
Weight of object (w) = ?
According to formula,
or, or, =
= = 16.62 × 10-1 = 1.662 m/s2
Hence, the acceleration due to gravity on moon is 1.662 m/s2.
Now,
Mass of a man (m)= 60 kg
Acceleration due to gravity (g) = 166.2 m/s2
Weight of man (F)= ?
We know,
F= mg
= 60 × 1.662
= 99.72 N
Hence, the weight of a man of 60 kg mass on the moon is 99.72 N.

Here,
We have,
Radius of the earth(R)= 6.4 × 103km= 6.4 × 106 m
Height of Mount Everest (h) = 8848 m= 8.848 × 103 m
Value of g at the surface (g) = 9.8 m/s2
Value of g at the top of Mt. Everest (g1) = ?
According to,
, so, = =
= =
= o.997 × 9.8
= 9.77 m/s2
The acceleration due to gravity at the top of Mount Everest is 9.77 m/s2.
Now, Mass of object (m) = 25 kg
Acceleration due to gravity (g) = 9.77 m/s2
Weight of object (w) = ?
We have,
W = mg
= 25 × 9.77
= 244.25 N

The weight of the body of mass 25 kg on the top of the Mount Everest is 244.25 N.

It means that the rate of change of velocity occurred in any body due to the force of gravity is 9.8 m/s.

When a body of mass "m" is dropped from "h" to the surface of the earth of mass "m" and Radius "R", its speed will increases as it comes near to the surface of the earth.
Let, height "h" be very small as compared to "R", so that height is neglected. The acceleration produced on a body is the acceleration due to gravity "g".
Force (F) = mass (m) × acceleration due to gravity (g)
or, F = m × g…………..(i)
But this force on the body i.e. due to the force of gravity
From Newton"s law of gravitation,
…(i)
From the equation (i) and (ii), we get,
or,
or, (where G and m are constant)

Here,

Mass of Jupiter(M) = 1.9 x 1027 kg

Radius of Jupiter (R) = 7.1 x 107 m

Accrleration due to gravity of jupiter (gj) = ?

Mass of a person on the Jupiter (W) = ?

Gravitational constant (G) = 6.67 x 10-11 N m2 / kg2

we have ,

g =\(\frac{G.M}{R^2}\)

= \(\frac{6.67×10^-11×1.9×10^27}{(7.1×10^7)^2}\)

= 25 m/s2

Again,

According to formula W = m.g

∴ w = 60 x 25

1500N

Therefore, the acceleration due to gravity is 25 m/s2 and the weight of a person is 1500N.

 

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