If the unit of mass is α kg, the unit of length is β metre and the unit of time is ‘γ ’ second, The magnitude of joule in the new system is (1cal=4.2J)

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4.2α2β2γ2 new units

α−1β−2γ2 new units

α−1β−2γ−2 new units

14.2 α−1β−2γ2 new units

answer is B.

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Detailed Solution

Joule is the unit of energy/work and its dimensional formula is ML2T-2N1U1=N2U21 Joule =N2 new units1M1L12T1-2=N2 M2L22T2-21N2=M2M1L2L12T2T1-2 1N2=α KgKgβ metmet2γ secsec-2 N2=α−1β−2γ2 new units

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