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Calculate the value of acceleration due to gravity that is 9.8m/S2​

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\rm \large \bf{ \color{darkviolet}{Question}}

\rm{calculate \: the \: value \: of \: acceleration \: due \: to \: gravity}

\bold{that \: is \: 9.8}

\rm \large \bf{ \color{darkviolet}{Answer}}

If we drop a body (say a stone ) of mass m from a distance R from the centre of the earth of mass M , then the force exerted by the earth on the body is given by universal law of gravitation as :

\large \bf{ \color{blue}{F = G \times \frac{M \times m}{ {R}^{2} }}}

\bf{ \color{blue}{G = Gravitational \: constant}}

This force is exerted by earth produces acceleration in the stone due to which the stone moves DOWNWARDS .

We Also Know That :-

\bf{ \color{red}{Force = Mass \times Acceleration}}

\red \longrightarrow \bf{ \color{red}{F = m \times a}}

\bf{ \color{red}{accelaration \: of \: stone \: (a) = \frac{F}{m} }}

Putting the values of F in the above equation

We get,

\bf{ \color{green}{acceleration \: a = \frac{G \times M \times m}{ {R}^{2} \times m }}}

\bf{ \color{green}{so \: \: \: \implies \: \: \: \: a = \frac{G \times M }{ {R}^{2}}}}

The acceleration produced by the earth is known as acceleration due to gravity and represented by the symbol (g) . So by WRITING 'g' in place of 'a' in the above equation.

We get,

\bf{ \color{blue}{Acceleration \: due \: to \: gravity \: (g) = G \times \frac{M}{ {R}^{2} }}}

where ,

G = Gravitational constant

M = Mass of the body

R = radius of the earth

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This is the formula for calculating the acceleration due to gravity on or NEAR the surface of the earth.

To calculate the value of g ,we should put the values of G, M and R in the above formula.

Now,

\bf{ \color{red}{Gravitational \: Constant \: G = 6.7 \times {10}^{ - 11} \: N{m}^{2}/ {kg}^{2}}}

\bf{ \color{red}{Mass \: of \: Earth \: M = 6 \times {10}^{24} \: kg}}

\bf{ \color{red}{Radius \: of \: the \: earth \: R = 6.4 \times {10}^{6} \: m}}

Putting these values of G , M and R in the above formula . We get,

\longrightarrow \large\bf{ \color{darkblue}{g = \frac{6.7 \times {10}^{ - 11} \times 6 \times {10}^{24} }{{(6.4 \times {10}^{6})}^{2} }}}

\longrightarrow \large\bf{ \color{darkblue}{g = \cancel\frac{6.7 \times {10}^{ - 11} \times 6 \times {10}^{24} }{{(6.4 \times {10}^{6})}^{2} }}}

\longrightarrow \bf{ \color{darkblue}{g = 9.8 {m/s}^{2}}}

Thus the value of acceleration due to gravity is 9.8m/s².

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Note :-

  • Sometimes to make the calculation easy the value of g is taken as a round figure of 10 m/s² .This is DONE just for the sake of convince.
  • This acceleration due to gravity acts in the direction of the line JOINING the body of the centre of the earth.


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