Where the strict application of any of the requirements of this chapter in the case of an exceptionally irregular, narrow, shallow or steep lot or other exceptional physical conditions would result in practical difficulty or unnecessary hardship that would deprive the owner of the reasonable use of the land or building involved, but in no other case, the Board of Appeals shall have the power, upon appeal, to vary or adjust the strict application of the regulations or provisions of this chapter. In all cases where the Board of Appeals authorizes the issuance of a building permit or occupancy permit under any of the above powers, it shall be the duty of said Board to attach such conditions and safeguards as may be required to protect the public health, safety, morals and general welfare.