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Acceleration due to gravity formula and problems

What is gravitational acceleration?

Acceleration of a freely falling bodies is called gravitational acceleration.The value of gravitational acceleration is 10 ms-².

 

Why value of g varies with altitude?

g

Above formula shows that the value of acceleration due to gravity g depends on the radius of the earth at its surface.The value of g is inversely  proportional to the square of the radius of the earth.But it does not remain constant.It decreases with altitude.Altitude is the height of an object or place above sea level.The value of g is greater at sea level than at the hills.

g with altitude

Consider a body of mass m at an altitude h as shown in figure.The distance  of the body from the center of the earth becomes R +h.

The formula of g (gravitational acceleration) is:

formula of gravitational acceleration

According to the above relation,we come to know that at a height equal to one earth radius above the surface of the earth,g becomes one fourth of its value on the earth.Similarly at a distance of two earth’s radius above the earth’s surface ,the value of g becomes one ninth of its value on the earth.Value of g on the surface of a celestial object depend on its mass and its radius.

The value of g on some of the objects is given below in table:

Object g(ms-2)
Sun    274.2
Mercury 3.7
 Venus 8.87
Moon 1.62
Mars 3.73
Jupiter 25.94

 

Value of g at centre of earth:

Value of g at centre of earth is zero.

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