Question

The mass of a planet is 6 x 10²⁴ kg and its diameter is 12.8 x 10³ If the value of gravitational constant be 6.7 x 10^-11 Nm²/kg², calculate the value of acceleration due to gravity on the surface of the planet. What planet could this be 

Answer 1

g = GM /R²
g (acceleration due to gravity) = ?
G (Gravitational Constant) = 6.7 × 10⁻¹¹ Nm² kg⁻²
M (mass of the planet) = 6 × 10²⁴ kg
R (radius of planet) = 6.4 ×10⁶ m    
(Diameter of the planet = 12.8 × 10³ × 2 × 1000 = 6.4 ×10⁶ m)
g = GM /R²
g = `(6.7 xx 10^-11 xx 6 xx 10^24)/(6.4 xx 10^6)^2` = `(6.7 xx 10^-11 xx 6 xx 10^24)/(6.4 xx 10^6)^2`  `(10^(24-11)=10^13)` = `(6.7 xx 6 xx 10^13)/(6.4 xx 6.4 xx 10^12)`   `(10^(13-12)=10) = 0.98 xx 10 = 9.8  "m/s"^2`
Answer : 9.8 `"m/s"^2`
This planet is earth .