Step 1: Separate land smoothing from land grading.
Land grading is the heavier earthmoving operation that sets the overall design slope using scrapers and levellers, while land smoothing is the light finishing pass that only has to knock off small local high spots and fill shallow local low spots left after grading, so the tool needed here does not have to move large volumes of soil.
Step 2: Check each option against that light, wooden, drag type description.
A leveller board and a U-leveller are blade based implements generally used earlier, during the grading stage, to cut and move soil to grade, which is heavier work than smoothing. A buck scraper is a bigger earthmoving scraper pulled by a tractor, again meant for bulk cut and fill work, not fine finishing.
Step 3: Identify the tool built specifically for the finishing pass.
A float is a simple wooden plank or beam dragged flat across the field surface behind a tractor, and its whole purpose is to drag down small ridges and fill small depressions in a single light pass, which is exactly the wooden implement used for land smoothening.
\[ \boxed{Float} \]