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[tex]\tt{\huge{\blue{Explanation:}}}[/tex]
The formula of the relativistic mass of an object is
[tex]\boxed{m = \frac{m_{0}}{\sqrt{1 - (\frac{v}{c})^{2}}}}[/tex]
where:
m = relativistic mass
m₀ = rest mass
v = speed of an object
c = speed of light in vacuum
[tex]\tt{\huge{\red{Solution:}}}[/tex]
m₀ = 6 kg
v = 0.8c
[tex]m = \dfrac{m_{0}}{\sqrt{1 - (\frac{v}{c})^{2}}}[/tex]
[tex]m = \dfrac{\text{6 kg}}{\sqrt{1 - (\frac{0.8c}{c})^{2}}}[/tex]
[tex]m = \dfrac{\text{6 kg}}{\sqrt{1 - (0.8)^{2}}}[/tex]
[tex]m = \dfrac{\text{6 kg}}{\sqrt{1 - 0.64}}[/tex]
[tex]m = \dfrac{\text{6 kg}}{\sqrt{0.36}}[/tex]
[tex]m = \dfrac{\text{6 kg}}{0.6}[/tex]
[tex]\boxed{m = \text{10 kg}}[/tex]
Therefore, the relativistic mass of the object is 10 kg.
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