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
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B
5α−1β2γ2
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C
5α−2β−1γ−2
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D
5α−1β−2γ2
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Solution
The correct option is C5α−1β−2γ2 Joule is a unit of energy.
SI
New system
n1=5
n2=?
M1=1kg
M2=αkg
L1=1m
L2=βm
T1=1s
T2=γs
Dimensional formula of energy is [ML2T−2]. Comparing with [MaLbTc], we get a = 1, b = 2,c = -2
As n2=n1(M1M2)a(L1L2)b(T1T2)c =5(1kgαkg)1(1mβm)2(1sγs)−2=5γ2αβ2=5α−1β−2γ2