Q36 of 44 Page 9

A new system of units is proposed in which unit of mass is α kg, unit of length β m and unit of time γ s. How much will 5 J measure in this new system?

Given


New unit of mass = α kg


New unit of length = β m


New unit of time = γ s


Magnitude of energy in original system n = 5J


The dimensional formula for energy is given as



Now let the magnitude of U in the original system of units be n, and in the new system of unit be n’


Then



Where [M1L12 T1-2] and [M2L22 T2-2] are the dimensions in the original system of units and new system of units respectively.



Now in the original system of units M1 = 1 kg , L1 = 1 m and T1 = 1 s. In the new system of units we have M2 = α kg , L2 = β m and T2 = γ s.




Thus, 5 J of energy will measure in the new system of units.


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