1.

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.

Answer» (i) From
`m=(m_(0))/(sqrt((1-v^(2)//c^(2))))=(m_(0))/(sqrt(1-1//4))=(2m_(0))/(sqrt(3))`
(ii) momentum `=mc//2=(2m_(0))/(sqrt(3)).(c)/(2)=(m_(0)c)/(sqrt(3))`
(iii) total energy `=mc^(2)=(2m_(0))/(sqrt(3))c^(2)`
(iv) K.E. `=` total energy `-` rest mass energy
`=(2m_(0))/(sqrt(3))c^(2)-m_(0)c^(2)=m_(0)c^(2)[(2)/(sqrt(3))-1]`
`=(m_(0)c^(2))/(sqrt(3))(2-sqrt(3))`


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