A cartridge for an image forming apparatus comprising: a housing; a driving input member provided at the housing, the driving input member configured to be rotated by an externally supplied rotation driving force; a rotational member configured to receive the rotation driving force, which is transmitted from the driving input member, and be rotated thereby in a rotational direction; a detection protrusion which is provided on the rotational member to be rotatable in the rotational direction together with the rotational member and is disposed at a position away from a rotational center of the rotational member, the detection protrusion protruding from the rotational member away from the housing; and a cover attached to the housing, the cover having an opposite part that faces a portion of the rotational member from which the detection protrusion protrudes and a guide part formed on an inner surface of the opposite part of the cover, wherein the guide part is configured to guide the detection protrusion when the rotational member rotates; characterized by the detection protrusion including an elastic body comprising a distal end and being configured to abut at an initial position, which is a position before the rotational member is rotated, the opposite part of the cover wherein the opposite part of the cover is configured to elastically deform the detection protrusion when the detection protrusion is positioned in a state in which the detection protrusion abuts the opposite part of the cover and wherein the opposite part of the cover is configured to bend the distal end of the elastic body toward the upstream in the rotational direction when the detection protrusion is placed inside the guide part of the cover and positioned in a state in which the detection protrusion abuts the opposite part of the cover to determine whether the cartridge is a new one when the cartridge is installed in the image forming apparatus. a housing; a driving input member provided at the housing, the driving input member configured to be rotated by an externally supplied rotation driving force; a rotational member configured to receive the rotation driving force, which is transmitted from the driving input member, and be rotated thereby in a rotational direction; a detection protrusion which is provided on the rotational member to be rotatable in the rotational direction together with the rotational member and is disposed at a position away from a rotational center of the rotational member, the detection protrusion protruding from the rotational member away from the housing; and a cover attached to the housing, the cover having an opposite part that faces a portion of the rotational member from which the detection protrusion protrudes and a guide part formed on an inner surface of the opposite part of the cover, wherein the guide part is configured to guide the detection protrusion when the rotational member rotates; at an initial position, which is a position before the rotational member is rotated, the opposite part of the cover wherein the opposite part of the cover is configured to elastically deform the detection protrusion when the detection protrusion is positioned in a state in which the detection protrusion abuts the opposite part of the cover and