The United States of America dropped two atomic bombs on the Japanese cities of Hiroshima and Nagasaki in:

August 1945

*The correct answer is Option 2 - August 1945*

The world war ended when the United States dropped two atomic bombs on the Japanese cities of Hiroshima and Nagasaki in August 1945, causing Japan to surrender.

More information:

During the Second World War which lasted from 1939-1945, the USA dropped 2 nuclear bombs on Japan which caused immense destruction. The bomb dropped by the US on 6th August 1945 on Hiroshima was codenamed ‘Little Boy’ and the one dropped on Nagasaki was code-named ‘Fat Man’. The Fat Man was dropped on 9th August 1945. Yet, these bombs were very small in their destructive capacity (measured in terms of kiloton yield) as compared to the nuclear bombs that were to be available in the stockpiles assembled by the superpowers. The yield of Little Boy and Fat Man were 15 and 21 kilotons respectively. The 'Little Boy' was a gun-type fission bomb and used Uranium-235 whereas 'Fat Man' was an implosion-type fission bomb and used plutonium-239. By the early 1950s, the US and the USSR were already making thermonuclear weapons that had a yield between 10 and 15 thousand kilotons.  In other words, these bombs were a thousand times more destructive than the bombs used in Hiroshima and Nagasaki.