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Question

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
5αβ2γ2
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B
5α1β2γ2
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C
5α2β1γ2
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D
5α1β2γ2
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Solution

The correct option is C 5α1β2γ2
Joule is a unit of energy.
SI New system
n1=5n2=?
M1=1kgM2=αkg
L1=1mL2=βm
T1=1sT2=γs

Dimensional formula of energy is [ML2T2]. 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=5α1β2γ2

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