proton a is at rest and proton b is moving with great velocity which proton has greater mass
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Both protons 'a' and 'b' will have the same mass at rest. Let us consider it 'm'.
Then, while in motion, proton 'b' will have some velocity, due to which, there will be a change it its relativistic mass. Let us consider it 'n'.
Let us consider the speed of light 'c' and 'v' the speed of proton 'b'.
Therefore,
n = m ÷ [1 - (v^2/c^2)]
= m ÷ [(c^2 - v^2)/c^2]
= m[c^2/(c^2 - v^2)].
Since 'c^2 - v^2' will definitely have a lesser value than 'c^2', the final value inside the square brackets will be greater that 1. This means that 'n' will have a greater value that 'm'.
Hence, we conclude that the relativistic mass of proton 'b' will be greater that that of proton 'a'.
Then, while in motion, proton 'b' will have some velocity, due to which, there will be a change it its relativistic mass. Let us consider it 'n'.
Let us consider the speed of light 'c' and 'v' the speed of proton 'b'.
Therefore,
n = m ÷ [1 - (v^2/c^2)]
= m ÷ [(c^2 - v^2)/c^2]
= m[c^2/(c^2 - v^2)].
Since 'c^2 - v^2' will definitely have a lesser value than 'c^2', the final value inside the square brackets will be greater that 1. This means that 'n' will have a greater value that 'm'.
Hence, we conclude that the relativistic mass of proton 'b' will be greater that that of proton 'a'.
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