Question

The radius of the earth is 6.4 × 10⁶ m and the acceleration due to gravity at its surface is 9.8 m/s². If the value of the gravitational constant is 6.7 × 10⁻¹¹ Nm/kg² , calculate the mass of earth.​

Answer 1

Given,

Radius (R) = 6.4*10⁶ m

Acceleration due to gravity (g) = 9.8 m/s²

G = 6.67*10^-11

[ '^' means to the power ]

g = Gm/r²

9.8 = (6.67*10^-11)*m / (6.4*10⁶)²

9.8 = 6.67*10^-11*m / (40.96*10³⁶)

(9.8*40.96)*10³⁶ = 6.67*10^-11*m

401.408*10³⁶ = 6.67*10^-11*m

(401.408/6.67)*10³⁶-¹¹ = m

60.18*10²⁵ kg = m

The Mass is 60.18*10²⁵ kg.

(As it was difficult to use minus in subscript in mobile so I used ^ sign.]

I hope this helps.