Question

Q If the mass of the earth is M= 6 x 1024 kg , radius of the earth is R= 6.4 x 106 m and the value of G is 6.7 x 10-11 N m2/kg2 , calculate the value of acceleration due to gravity 'g' using the above formula.​

Answer 1

Answer :-

9.8m/s^2

Explanation :-

Given :

Mass of the earth = 6 × 10^24kg

Radius of the earth = 6.4 × 10^6

Universal gravitational force = 6.7 × 10^-11 Nm^2/kg

To Find :

Acceleration due to gravity,g = ?

Solution :

We know,

$\boxed{\sf{}g=G\dfrac{M}{r^2}}$

where,

g is acceleration due to gravity,

G is the Universal Gravitational Constant.

M is the mass of earth.

and r is the radius of the earth.

Put the values of G, M and R to get “g”

$\sf{}\implies g=\dfrac{6.7\times 10^{-11}\times 6 \times 10^{24}}{(6.4\times 10^5)^{2}}$

$\sf{}\implies g=\dfrac{40.2\times 10^{-11}\times 10^{24}}{6.4\times 10^5\times 6.4\times 10^6}$

$\sf{}\implies g=\dfrac{40.2\times 10^{-11+24}}{40.96\times 10^{6+6}}$

$\sf{}\implies g=\dfrac{40.2\times 10^{13}}{40.96\times 10^{12}}$

$\sf{}\implies g=0.98\times 10^{13-12}$

$\sf{}\implies g=0.98\times 10\times \dfrac{10}{10}$

$\sf{}\implies g=9.8m/s^2$

Therefore,the value of acceleration due to gravity of the earth is equal to 9.8m/s^2