Ground hogs are apparently remarkably tough for their size. i started with a .,17HMR and worked my way up through the Hornet, .223, and .22-250, to a .243. My go-to ground hog rifle for South Central PA (most shots are 225 yards or less) is my .223 CZ527 American shooting the 40g NBT @ 3650 fps.
How much gun is needed to leave them DRT? The answer is it depends on how old and how big they are. I have the most DRT kills with my .223 shooting the 40g Nosler Ballistic Tip @ around 3650 fps MV - that bullet just destroys them - they are dead before the sound gets there.
I've dropped young ones just out of the nest in the spring with the .17HMR DRT (Dead Right There). I like that cartridge around the barn and in the back yard of the house. Much bigger than that and the .17HMR will often leave them crawling off to die which I do not like.
Up to to ~9 or even 10lbs the Hornet with the 34g Midway DT (pushed into tiny groups by 13.3g Lil'Gun) kills them DRT hit in the boiler room. Heavier than that and the Hornet needs a head shot to avoid them crawling a few feet before the salute.
Up to 12 lbs (the biggest I've actually weighed) the .223 with a 40g NBT leaves them DRT out to 254 yards (the farthest I've shot one with it). The 40g NBT leaving the muzzle at 3650 has amazing terminal performance - when I see the hit (mostly at close range with the scope power at 4.5X) the ground hogs whole body expands like a grenade went off inside, then it collapses right in it's shadow. Not even a wiggle. When I get there they are usually ripped open from end to end like the interior pressure just burst them. Out at 225 to 250 yards the bullet doesn't take them apart that much but it leaves a softball size exit hole on 10lb and smaller GH. Bigger ones are just DRT.
That seems to be the optimum speed for that bullet. Out of my .22-250 (4,200 fps) it doesn't do as well. The 55g NBT (also at around 3650 fps) works well out of the .22-250. I'd rather shoot the 55g V-Max but for some reason I can't get the accuracy with that bullet that I can with the NBT.
The biggest ground hog I ever saw I shot with a 55g NBT @ just under 4,000 fps out of my .243 at just over 200 yards. I know I hit it hard, there was plenty of blood, but it crawled to it's (huge) hole and out of sight rather quickly. The rifle is dead on, I had a rock solid hold and the hit had to be right through the boiler room, but it did "not" drop where I could retrieve it, darn it. I "really" wanted to weigh that critter. I'm pretty sure it would have run to 14 or 15 lbs. It was huge.
I shot one (around 11 lbs - an estimate) with a 95g NBT out of the .243 while out Coyote hunting
. It took two shots to make sure it was dead. The bullet is a poor choice for ground hogs, it didn't expand much at all, but I took the shot anyway.