Question

the hight at which The acceleration due to gravity becomes R/9 in turm of R the radius of the earth is

Answer 1

we know,
g = g°/(1 + h/R)²

where, g is acceleration due to gravity at h height , g° is acceleration due to gravity initial . ( at earth ) .
h is heght from the earth surface.
R is radius of earth .

here,
h = R/9
g = ?

g = g°/( 1 + R/9R)² = 81g°/100

hence, acceleration due to gravity at height R/9 is 81g°/100

Answer 2

Hey there!

For finding radius we can apply this formula:

g = g°/(1 + h/R)² 

here,
g is acceleration at Height(h)
g° is acceleration at  initial gravity
h is height 
R is radius .

Now, see the given data:
i.e h = R/9 

Then,
g = g°/( 1 + R/9R)²
   = 81g°/100  ← (Ans)