If Planck's constant (h) and speed of light in vacuum (c) are taken as two fundamental quantities, which
one of the following can, in addition, be taken to express length, mass and time in terms of the three
chosen fundamental quantities ?
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Answer:
Correct option is
C
(i) , (ii) and (iv)
(h)=
[T
−1
]
[ML
2
T
−2
]
=[LT
−1
]
for mass, let M=C
a
h
b
G
c
[ML
0
T
0
]=[LT
−1
]
a
[ML
2
T
−1
]
b
[M
−1
L
3
T
−2
]
c
Using the principle,
b−c=1⟶(1)
a+2b+3c=0⟶(2)
−a−b−2c=0⟶(3)
So, a=
2
−1
also a=
2
1
Hence, M=C
1/2
h
1/2
G
−1/2
⇒M=
G
Ch
Similarly, for length L=
C
3
hG
and T=
C
5
hG
∴ Plank's length =
C
3
Gh
; Plank's time =
C
5
Gh
and Plank's Mass =
G
Ch
Hence, (a), (b), (d) are correct options.
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