Answer:
0.4 times the radius of moon
Step-by-step explanation:
gravity on moon is equal to the one sixth of gravity on earth.
g' = g / 6
where, g' is the gravity on moon and g be the gravity on earth.
As the earth shrinks, the mass of earth remains same.
The acceleration due to gravity is inversely proportional to the square of radius of planet.
g' ∝ 1/R'² .....(1)
Where, R' is the radius of moon.
g ∝ 1/R² ..... (2)
Where, R be the radius of earth.
Divide equation (1) by (2)
g / g' = R'² / R²
Put g' = g / 6
6 = R'² / R²
2.5 = R' / R
R = R' / 2.5 = 0.4 R'
Thus, the radius of earth should be 0.4 times the radius of moon.