No pension shall be paid to the surviving husband of a deceased member of the pension corporation unless he is and continues to remain dependent upon the income which the member was receiving at the time of her death, nor unless he is and continues to remain physically or mentally incapable of pursuing a gainful occupation, nor shall any pension be paid to a minor child under the age of sixteen years of a female member unless the child is dependent upon the income which the member was receiving at the time of her death and continues to be so dependent. The board of trustees shall determine the question of the dependency of the surviving husband or minor child as well as the ability of a surviving husband to pursue a gainful occupation.