Acceleration due to gravity
Today post is all about acceleration due to gravity, In this post you will learn, what is acceleration due to gravity ? How its value is 9.8 m/s², acceleration due to gravity has fixed value, Why and how its value varies at different point location and due to Earth rotation, How acceleration due to gravity is a gravitational field, You will learn all concepts about of acceleration due to gravity, so lets start.
What is acceleration due to gravity ?
Gravity is a force with which Earth attract every other object towards it centre. Earth has created this gravity around its surrounding. This property of the Earth is due to heavy mass of the Earth, Because compare to the Earth mass, all other objects masses are small near its surrounding, Hence all other masses falls towards centre of the Earth.
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| Acceleration due to gravity |
From the figure above Earth is pulling you with force mg, you also know from the law of gravitation force between two masses, you can refer previous post for Gravitational force the value of force between Earth and man shown in figure will be F= GMₑm/(Rₑ + h)²
here value of h is very small compare to radius of Earth Rₑ so h is neglected,
Hence F = GMₑm/Rₑ² , Now both force will be equal as per statement.
GMₑm/Rₑ² = mg or g = GMₑ/Rₑ² , this is important formula where G is universal gravitational constant G = 6.67x10⁻¹¹ Nm²/kg², Rₑ is radius of Earth approx Rₑ = 6400 km,
Rₑ = 6.4x10⁶ m , Mₑ is mass of Earth approx Mₑ = 6x10²⁴ kg .
Now after putting all the values in above formula g = 6.67x10⁻¹¹x6x10²⁴/(6.4x10⁶)²
g = 9.8 m/s², remember this value of g is near the earth surface only.
Suppose if h is very high then you can't neglect value of h, so in this case g = GMₑ/(Rₑ + h)², Now as the value of h increases then value of g will decreases, So you can't say value of g is constant.
On increasing the value of h from the surface of the Earth value of g will decrease. You will see how the value of g decreases as moving from the surface of the Earth in this post later.
Now see below picture and find weight.
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| Weight at Mars |
