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A new system of units is proposed in which unit of mass is α kg, unit of length is β m and unit of time is γ s. What will be value of 5 J in this new system?
  • a)
    5αβ2γ−2
  • b)
    −1β-2γ2
  • c)
    −2β−1γ−2
  • d)
    −1 β2γ2
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A new system of units is proposed in which unit of mass is α kg,...
Joule is a unit of energy.

Dimensional formula of energy is [ML2 T−2].
Comparing with [Ma Lb Tc], we get a = 1, b = 2,c = -2
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A new system of units is proposed in which unit of mass is α kg,...
Defined as the mass of a specific number of atoms or molecules. This proposed unit of mass is called the mole, and it is defined as the amount of substance that contains the same number of entities as there are atoms in 12 grams of carbon-12. The unit of length in this system is the meter, and it is defined as the distance traveled by light in a vacuum during a specific interval of time. The unit of time is the second, and it is defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom. This system of units is called the International System of Units (SI), and it is widely used in science and technology worldwide.
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A new system of units is proposed in which unit of mass is α kg, unit of length is β m and unit of time is γ s. What will be value of 5 J in this new system?a)5αβ2γ−2b)5α−1β-2γ2c)5α−2β−1γ−2d)5α−1β2γ2Correct answer is option 'B'. Can you explain this answer?
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