What work has to be performed in order to increase the velocity of a particle of rest mass `m_0` from `0.60c` to `0.80c`? Compare the result obtained with the value calculated from the classical formula.

Explanation

The work done is equal to change in kinetic energy which is different in the two cases Classically i.e. in nonrelativistic mechanics, the change in kinetic energy is
`1/2m_0c^2((0*8)^2-(0*6)^2)=1/2m_0c^20*28=1*14m_0c^2`
Relativistically it is,
`(m_0c^2)/(sqrt(1-(0*8)^2))-(m_0c^2)/(sqrt(1-(0*6)^2))=(m_0c^2)/(0*6)-(m_0c^2)/(0*8)=m_0c^2 (1*666-1*250)`
`=0*416m_0c^2=0*42m_0c^2`