Mass `m=(m_(0))/(sqrt(1-(v^(2))/(c^(2))))` as a function of a velocity is shown in the graph. `m_(0)` is the rest mass of the system. The kinetic energy of system is given as `K=mc^(2)-m_(c)C^(2)`
Choose correct option (s)

Options

A. If a system is moving with speed `v=0.5c`, the mass of system is increased by `15.5%`.
B. Electrons in Cornell university synchrotron reach a velocity of `v=0.8c`. The mass of these electrons are approximately `(5/3)` time the set mass of electron
C. The Beatron a proton accelerator generates the accelerated protons with kinetic energy `10^(-9)` Joules. The mass of accelerated protons is `8.68` time the acutal mass of proton aproximately `(m_(p_(0))=1.67xx10^(-27)kg)`
D. If the kinetic energy of particle is equal to its rest mass energy then speed of particle is `0.75c` approximately.

Answer

A, B

Explanation

(C) `M/(M_(0))=(Mc^(2))/(M_(0)c^(2))=(K+M_(0)c^(2))/(M_(0)c^(2))=1+(10^(-9))/(1.67xx10^(-27)xx9xx10^(20))~~7.68`
(D) `Mc^(2)=M_(0)c^(2)+K+2m_(0)c^(2)`
`impliesM=2M_(0)`
`implies(M_(0))/(sqrt(1-(v^(2))/(c^(2))))=2M_(0)`
`implies1=4-(4v^(2))/(c^(2))`
`impliesv^(2)=(3c^(2))/4impliesv=(sqrt(3))/2 c=0.866c`