Question

at what distance below the surface of the Earth the acceleration due to gravity decrease by 10% of its value at the surface given radius of earth is 6400 km answer 640km​

Answer 1

Answer:

346.19 km

Explanation:

m = Mass of the Earth =  5.972 × 10²⁴ kg

G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²

r = Radius of Earth = 6400 km

$g=G\frac{M}{r_1^2}$

Now

$g_n=g-0.1g\\\Rightarrow g_n=0.9g$

$0.9g=G\frac{M}{r_2^2}$

Dividing both the equations

$\frac{0.9g}{g}=\frac{G\frac{M}{r_2^2}}{G\frac{M}{r_1^2}}\\\Rightarrow 0.9=\frac{r_1^2}{r_2^2}\\\Rightarrow 0.9=\frac{6400^2}{r_2^2}\\\Rightarrow r_2^2=\frac{6400^}{0.9}\\\Rightarrow r_2=\sqrt{\frac{6400^2}{0.9}}\\\Rightarrow r_2=6746.19\ km$

The acceleration due to gravity cannot decrease by going below the Earth's. When going below the surface the accelration due to gravity increases. So, the acceleration due to gravity will decrease while going above the surface.

Hence, the distance above the surface would be 6746.19-6400 = 346.19 km