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Question

If velocity v, force F and energy E are taken as fundmental units, then dimensional formula for mass will be

A
v2F0E
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B
v2F2E
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C
v2F0E2
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D
vF2E
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Solution

The correct option is A v2F0E
Let [m]=[vaFbEc]
[m]=[v]a[F]b[E]c
[ML0T0]=[LT1]a[MLT2]b[ML2T2]c
[ML0T0]=[M(b+c)L(a+b+2c)T(a2b2c)]
Equating the power of dimensions we get
a=2,b=0,c=1
Thus we have [M]=[v2F0E]

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