The velocity of a particle at which the kinetic energy is equal to its rest mass energy is

Options

A. `25.98xx10^(8)` m/s
B. `2.598xx10^(8)` m/s
C. `2.895xx10^(8)` m/s
D. `2.985xx10^(8)` m/s

Answer

B

Explanation

Given, `m_(0) c^(2)=1/2 m_(0) v^(2)`
`:. E=mc^(2)=2m_(0) c^(2)`
`:. m=2 m_(0)`
Now, `m=m_(0)/sqrt(1-v^(2)/c^(2)) implies 2m_(0) = m_(0)/sqrt(1-v^(2)/c^(2))`
`implies 4=1/(1-v^(2)/c^(2)) implies 1/4 =1 - v^(2)/c^(2)`
`:. v/c=sqrt(3)/2`
`:. v=(1.732xx9xx10^(8))/2`
`=2.598xx10^(8) m//s`