5. show that the value of 'g' io 9. 8 m/s2
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As we know By Newton's law of gravitation
Gravitational force between any two mass present anywhere in the universe is given by
F=GMmr²
Also we know that By Newton's second law motion
F=ma
Now, as these force are equal on same body
Then,
ma=GMmr²
a=GMr²
This gives acceleration due to gravity on any planet
For earth we have
Radius of earth (R)= 6.37×106 m
Mass of earth (M)= 5.97×1024 Kg
Gravitational constant (G)= 6.673×10−11 Nm²/Kg²
‘a' becomes ‘g'
g=GMR²
By putting the values of 'G' 'M' & ' R' we have
g=6.673×10−11×5.97×10246.37×106²
g=9.810665m/s²
g=9.8m/s² ( up to one decimal )
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