For example if a new nation is formed (e.g. South Sudan) then what are the necessary conditions a nation must satisfy so that they could be eligible for getting inducted into U.N. ??
As shown in Michael_B's reference About UN Membership
Membership in the Organization, in accordance with the Charter of the United Nations, “is open to all peace-loving States that accept the obligations contained in the United Nations Charter and, in the judgment of the Organization, are able to carry out these obligations”. States are admitted to membership in the United Nations by decision of the General Assembly upon the recommendation of the Security Council.
The procedure is briefly as follows:
- The State submits an application to the Secretary-General and a letter formally stating that it accepts the obligations under the Charter.
- The Security Council considers the application. Any recommendation for admission must receive the affirmative votes of 9 of the 15 members of the Council, provided that none of its five permanent members — China, France, the Russian Federation, the United Kingdom of Great Britain and Northern Ireland and the United States of America — have voted against the application.
- If the Council recommends admission, the recommendation is presented to the General Assembly for consideration. A two-thirds majority vote is necessary in the Assembly for admission of a new State.
- Membership becomes effective the date the resolution for admission is adopted.
The necessary conditions are listed in the UN Charter. For example, article 2 of chapter 1 says
The Organization and its Members, in pursuit of the Purposes stated in Article 1, shall act in accordance with the following Principles.
- The Organization is based on the principle of the sovereign equality of all its Members.
- All Members, in order to ensure to all of them the rights and benefits resulting from membership, shall fulfill in good faith the obligations assumed by them in accordance with the present Charter.
- All Members shall settle their international disputes by peaceful means in such a manner that international peace and security, and justice, are not endangered.
- All Members shall refrain in their international relations from the threat or use of force against the territorial integrity or political independence of any state, or in any other manner inconsistent with the Purposes of the United Nations.
- All Members shall give the United Nations every assistance in any action it takes in accordance with the present Charter, and shall refrain from giving assistance to any state against which the United Nations is taking preventive or enforcement action.
- The Organization shall ensure that states which are not Members of the United Nations act in accordance with these Principles so far as may be necessary for the maintenance of international peace and security.
- Nothing contained in the present Charter shall authorize the United Nations to intervene in matters which are essentially within the domestic jurisdiction of any state or shall require the Members to submit such matters to settlement under the present Charter; but this principle shall not prejudice the application of enforcement measures under Chapter Vll.