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 (R_{p}) of the earth is less than the equatorial radius (R_{e}).
i.e. R_{p} < R_{e }
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.,g_{p} > g_{e }Because R_{p}< R_{e}
Since g_{p} > g_{e} 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 ∝
AsSolukhumbu lies at thehigher 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
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. But in absence of air there is nothing to resist their falling so they fall at the same rate 9.8
 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.
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.
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/s^{2}.  Its unit is Nm^{2}/kg^{2}. 
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.
We have,
Mass of the moon (M)= 7.2 × 10^{22} kg
Radius of the moon (R) = 1.7 × 10^{6} m
Mass of a man (m) = 60 kg
Weight of object (w) = ?
According to formula,
or, or, =
= = 16.62 × 10^{1} = 1.662 m/s^{2}
Hence, the acceleration due to gravity on moon is 1.662 m/s^{2}.
Now,
Mass of a man (m)= 60 kg
Acceleration due to gravity (g) = 166.2 m/s^{2}
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 × 10^{3}km= 6.4 × 10^{6} m
Height of Mount Everest (h) = 8848 m= 8.848 × 10^{3} m
Value of g at the surface (g) = 9.8 m/s^{2}
Value of g at the top of Mt. Everest (g1) = ?
According to,
, so, = =
= =
= o.997 × 9.8
= 9.77 m/s^{2}
The acceleration due to gravity at the top of Mount Everest is 9.77 m/s^{2}.
Now, Mass of object (m) = 25 kg
Acceleration due to gravity (g) = 9.77 m/s^{2}
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.
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 10^{27} kg
Radius of Jupiter (R) = 7.1 x 10^{7} m
Accrleration due to gravity of jupiter (g_{j}) = ?
Mass of a person on the Jupiter (W) = ?
Gravitational constant (G) = 6.67 x 10^{11} N m^{2} / kg^{2}
we have ,
g =\(\frac{G.M}{R^2}\)
= \(\frac{6.67×10^11×1.9×10^27}{(7.1×10^7)^2}\)
= 25 m/s^{2}
Again,
According to formula W = m.g
∴ w = 60 x 25
1500N
Therefore, the acceleration due to gravity is 25 m/s^{2} and the weight of a person is 1500N.

Which of the following statement is correct for acceleration due to gravity?
It is inversly proportional to the square of radius
It is directly proportional to the square of radius
None of above
It is inversly proportinal to the square of mass

The value of g on the surface of the earth is ......
Can't say
independent of the mass of the earth and radius of the earth
depend on the mass of the body
independent of the mass of a body

Acceleration due to gravity is .....at poles than in equator.
more
less
equal
Can't say

If there is no air resistance then all the bodies fall together irrespective of their ....
amount of body
masses
weight
pressure

The value of g on the surface of the earth is ......
9.8 m/s^{2}
9.7 m/s^{2}
7.8 m/s^{2}
8.8 m/s^{2}

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edeeaaa 
Jan 02, 2017 
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DevilExplain the reason that the mass of a substance is constant but its weight is different at different places. 
Jan 01, 2017 
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Anjali RanaThe weight of an object is more at the bottom of Mt.Everest than at the top.Why? 
Dec 31, 2016 
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Sweta KattelA large stone of 20 kg and a small stone of 5 kg are dropped simultaneously from a certain height . Which one will reach the ground first ? Why ? 
Dec 28, 2016 
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