We can’t deal the question with classical mechanics approach as as when you calculate v with this approach it will come out to be more than speed of light in vacuum i.e. that violates the special theory of relativity.

So we have to solve these types of question taking relativistic approach.

As we know the gain in Kinetic energy is due to change in mass

As we know the moving object appears to be heavier in the moving frame that’s because of Lorentz transformation known as apparent mass which is given by

Where , V is velocity of moving object and C is speed of light in vacuum i.e.

And is mass at rest i.e.=

K.E=

a) So 10for 1 eV i.e.

As

Squaring both side and using binomial as we know using binomial expansion we know we can write

when

V=

b) Similarly for 10KeV i.e.

As

Squaring both side and using binomial as we know using binomial expansion we know we can write

when

V=

c) Similarly for 10KeV i.e.

As