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An object of rest mass 6 kg is moving with a speed of 0. 8c. Is effective mass is

Sagot :

[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]

Listing the given values

m₀ = 6 kg

v = 0.8c

Solving for m

[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.

[tex]\\[/tex]

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