The YouGov survey, commissioned by the Mental Health Foundation, found that more parents thought their children were more worried about the US President (28 per cent) than nuclear war (24 per cent).
A much bigger concern, however, was the threat of terrorism, with nearly half (45 per cent) of children in Yorkshire “anxious” about it, compared to a national average of 41 per cent.
Six in ten parents of those who were anxious noticed they had started asking a lot more questions.
In one in ten cases, children were so concerned their parents said they had asked to avoid using public transport or going to busy public places.
A further eight per cent said their children had nightmares.
Threats posed by global warming and climate change, also concerned 29 per cent of children, according to the poll.
Child psychology expert Dr Camilla Rosan of the Mental Health Foundation, said the survey, which quizzed more than 1,800 parents in the UK, including 170 in Yorkshire, revealed “widespread anxiety” among children, especially about terrorism.
Dr Rosan said: “We often forget that distressing world events can have a significant impact on the mental health of our children.
“This is especially true in the digital age where it’s no longer possible to shield our children from worrying or scary news.
But she said there was much they could do to help assure children, including letting them know the facts, but also putting things into perspective and letting them know they are safe.
She added: “Anxiety about scary news events is normal, but not something children have to deal with alone.
“Parents can really help tackle problems early and support good mental health for their children by talking about these issues in an open and honest way.”
The charity, which was founded in 1949 and works to prevent mental health problems, has released useful guidelines for parents on their website.