Dragging furniture across one’s floor or ground: 
It is permitted to drag an average size table, chair, or bed over any floor, including an earth floor, so long as one has no intent to form a ditch in the earth and doing so does not inevitably cause the ditch to be formed. This applies even if one has other furniture available and does not need specifically to drag this piece of furniture.
If the furniture is very heavy and dragging it on the ground will certainly cause a ditch to be formed, it is forbidden to be done, even if one has no intention to form the ditch. Furthermore, such furniture may not even be dragged inside one’s house over a tiled floor, due to a decree that one may come to drag it on an earth floor. [If however the ground of all the houses of one’s city is tiled, whether with tiles, wood, or other material, it is permitted to drag furniture such as a chair, bed or table over the floor. [Regarding if moving a heavy closet and the like contains a Muktzah prohibition, see Q&A!]
It is permitted to drag furniture over the floor of one’s house. It is forbidden to drag furniture over an earth floor if doing so will inevitably cause a ditch to be dug.
May one push a baby carriage over an earth floor, such as over the ground outside, in a place where there is an Eiruv?
Yes. This is permitted even if one pushes the carriage to the side and makes a ditch in the earth. It is forbidden to push a stroller in an area that does not have an Eiruv.
May one push a wheel chair over an earth floor?
Are closets and book cases which are designated to a specific area allowed to be moved?
Many Poskim forbid moving closets and book cases due to considering the closets as Muktzah. However seemingly this matter is subject to the same dispute regarding if items of sentimental value are Muktzah in which some learn that according to Admur it is permitted.
 Which is forbidden due to the prohibition of Choreish/plowing.
 As the rule by unintended transgressions is that if the transgression is inevitable occurrence of one’s action then it is as if one intended to do so, and is hence forbidden to be done. Now although this inevitable forming of the ditch is being done through an irregularity, as one is only liable for digging when it is done with its proper tools, as well as this formation is not beneficial for one’s ground but is rather destructive, as well as that it is a Melacha Sheiyno Tzarich Legufa, nevertheless it is Rabinically forbidden to be done. [ibid]
 Vetzaruch Iyun, as if even on an earth floor it is a mere Rabbinical prohibition, would it not violate the rule “we do not make decrees upon decrees” to decree that even on tiled floors it may not be dragged?
 In Ketzos Hashulchan 146/27 he writes majority of the city houses, and so seems to be also the intent here. Vetzaruch Iyun in why he changed the wording.
 Ketzos Hashulchan 146/26; Biur Halacha “Veyeish Machmirim”
 Ketzos Hashulchan 146 footnote 52
 Doing so does not form ditches within the earth but rather presses it more in. There is likewise no prohibition of “mundane act” involved in pushing a baby carriage outside, as there is with regards to carrying someone in a chair on Yom Tov [522/3], as it is very difficult to carry a baby otherwise, and there is thus no longer worry that doing so belittles Shabbos. [ibid]
 SSH”K 28/42
 Piskeiy Teshuvos 337/1
 M”B 308/8; SSH”K 20/22
 See Volume 1 “The Laws of Muktzah” Halacha 4 Q&A!
 Piskeiy Teshuvos 308/2. However see footnote there.
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