The correct answer is C) Fir-tree design. The fir-tree design is considered the most satisfactory method for attaching turbine blades to the rotor disk. This is because the fir-tree shape provides a secure and reliable connection, allowing the turbine blades to withstand the high stresses and forces experienced during operation. The fir-tree design distributes the load evenly across the attachment point, reducing the risk of failure compared to other attachment methods like pinning or locking tabs. The other options, such as the pinning design (A) or retaining ring design (D), are generally less preferred for turbine blade attachments due to their potential for stress concentration and increased risk of failure under the demanding operating conditions.