The lower yield point for an iron that has an average grain diameter of 1 × 102 mm is 230 mpa. at a grain diameter of 6 × 103 mm, the yield point increases to 275 mpa. at what grain diameter will the lower yield point be 310 mpa? \

This problem is related to strength of materials associating yield point to grain diameter. The formula to be used to determine the corresponding grain diameter at 310 MPa (low yield point) is expresed as 

y =  yo + k /√x
where y is the low yield point at MPa, x is the grain diameter in mm and k is the constant of proportionality. 

Substituting each conditions to the equation: 

(1) y = yo + k /√(1x10-2)
   230 = yo + 10k

(2) y = yo + k /√(6x10-3)
    275 = yo + 12.90k

Using the two equations, we can get yo = 75 MPa and k is equal to 15.5 Mpamm^1/2 .

Substituting to find the answer,

310 = 75 + (15.5)/√x
x = 0.00435 mm = 4.35 x 10-3 mm