Question

how much below the earth surface the acceleration due to gravity reduces to 36%

Answer 1

Acceleration due to gravity below the Earth's surface is given as,
g' = g (1 - d / R)   ......... (1)
where,
g' is the new acceleration due to gravity
d is the depth below the Earth's surface
R is the radius of the Earth
Now, if the acceleration due to gravity reduces to 36% below the Earth's surface then
g' = 36 % of g
g' = (36/100) x g
Put this value in equation (1).
(36/100) x g = g (1 - d / R) 
0.36 = 1 - d / R
d / R = 1 - 0.36
d = R (0.64)    .......... (2)
We know that,
R = Radius of Earth = 6.4 x 10⁶ m
Put this value in equation (2), 
d = (6.4 x 10⁶) (0.64)
d = 4096000 m
d = 4096 km
which is the required answer.

Answer 2

Answer is 4096 km.

I hope this will help you!!