Which instrument is specifically designed to extract first and second mandibular molars?

The instrument specifically designed to extract first and second mandibular molars is the cow horn forceps. This type of forceps is uniquely shaped to adapt to the anatomy of the mandibular molars, particularly the roots, which are typically bifurcated. The designated design of the cow horn forceps allows for effective engagement of the tooth and sufficient leverage to facilitate extraction, making them particularly effective for molars in the mandible.

Other instruments listed, such as the bonefile, mallet, and rongeurs, serve different purposes in dentistry. A bonefile is used for smoothing bone surfaces, a mallet is generally used in conjunction with chisels to trim or shape bone, and rongeurs are used to remove bone or tissue rather than to extract teeth. Thus, the cow horn forceps are the correct choice for the specific task of removing first and second mandibular molars due to their design and function tailored for that purpose.