A particle of rest mass `m_(0)` moves with a spess `c//2` . Calculate its
(i) mass (ii) momentum (iii) total energy (iv)K.E.

Explanation

Here, rest mass of particle `=m_(0)`
speed, `upsilon=c//2`
Accordin to theory of relativity, variation of mass with velocity is given by
`m=(m_(0))/(sqrt(1-upsilon^(2)//c^(2)))`
`m=(m_(0))/(sqrt(1-((c//2)^(2))/(c^(2))))=(m_(0))/(sqrt(1-(1)/(4)))=(2m_(0))/(sqrt(3))`
Momentum of particle
`p=m upsilon=(2)/(sqrt(3))m_(0)xx(c)/(2)=(m_(0)c)/(sqrt(3))` Total energy `E=mx^(2)`
`(2m_(0))/(sqrt(3))c^(2)=(2m_(0))/(sqrt(3))c^(2)`
kinetic energy `=` Total energy `-` rest mass energy
`=(2)/(sqrt(3))m_(0)c^(2)-m_(0)c^(2)``=m_(0)c^(2)[(2)/(sqrt(3))-1]=m_(0)c^(2)[(2)/(1.732)-1]`
`=m_(0)c^(2)(1.154-1)`
`=0.154m_(0)c^(2)`