Question

Prove that acceleration due to gravity on earth is 9.8 m/s2.
(Given : G = 6.67 X 10-11 Nm2/kg, mass of earth = 6 X 10 24 kg
Radius of earth = 6.4 X 10⁶m)​

Answer 1

Explanation:

let mass of an object be $m$.

let the mass of earth be $m_E$.

let the radius of earth be $r$.

we know that,

$F = G \frac{m \times m_E}{r^2}$

also,

$F = ma$

therefore,

$ma = G \frac{m \times m_E}{r^2}$

=> $a = G \frac{m_E}{r^2}$

given,

$G = 6.67 \times 10^{-11} \frac{N {m}^{2} }{ {kg}^{2} } \\ m_E = 6 \times 10^{24}kg \\ r = 6.4 \times 10^6m$

therefore,

$a = G \frac{m_E}{r^2}$

=> $a = 6.67 \times {10}^{ - 11} \times \frac{6 \times {10}^{24} }{(6.4 \times 10^{6} )^{2} } \frac{m}{ {s}^{2} }$

=> $a = \frac{4.02 \times {10}^{13} }{40.96 \times {10}^{12} } \frac{m}{ {s}^{2} }$

=> $a = 9.77m/s^2$

=> $a = 9.8m/s^2$

so proved!

acceleration due to gravity is $9.8m/s^2$