A nuclear bomb here and there can't do much harm, can it?
With all the cold war nuclear weapon testings done by both superpowers (USSR and USA) we are led to believe so. I mean, the soviets developed a 100 megaton nuclear weapon, named Tsar Bomb. Due to it's extraordinary power, it was reduced to 50 megatons, and still was 10 times stronger than all of the explosives used in WW2 combined. The mushroom cloud upon detonation reached a height of 60 kilometers and the blast force could be felt all the way to Finland, even braking some windows there. You can read more about Tsar Bomb in the wikipedia article So if that beast didn't tear Earth apart, what will?
There's a budding conflict between India and Pakistan. Both countries have an estimate of 50 nuclear weapons, similar in power to the Hiroshima bomb back in WW2. Researchers have chosen that scenario for testing. Michael Mills and his colleagues of the University of Colorado at Boulder, used computer models to estimate the amount of damage that would be done globally. The results suggested a world-wide cataclysm. Firstly, due to the large population of India, hundreds of millions of people would starve because of the ruined agriculture. Then, of course, there are the blast victims, those fallen ill to radiation, and those who will in the many years to come.
So what about the rest of the world? No, we won't be safe. The burning rubber, plastic and other chemical products would emit clouds of black soot up to 80 kilometers into the skies. This would greatly damage the ozone layer all around the world, especially in the polar regions. The ozone layer protects us from the many dangerous rays, particularly ultraviolet, incoming from space. With the ozone layer diminished, more rays would reach us, increasing the damage done to human DNA by 213 percent. The ozone layer would return to it's normal state only in 5-10 years.
The research showed how a small-scaled conflict can affect the whole world. We can sleep easily on that, though. If such great powers USA and the Soviet Union didn't nuke each other 40 years ago, there is almost no chance that will happen in much weaker countries. But, who knows. Time changes everything.