if g c and h are fundamental physical quantity then express mass
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Answer:
Let l∝c
x
h
y
G
z
;l=kc
x
h
y
G
z
where k is a dimensionless constant and x, y and z are the exponents.
Equating dimensions on both sides, we get
[M
0
LT
0
]=[LT
−1
]
x
[ML
2
T
−1
]
y
[M
−1
L
3
T
−2
]
z
=[M
y−z
L
x+2y+3z
T
−x−y−2z
]
Applying the principle of homogeneity of dimensions, we get
y−z=0 ....(i)
x+2y+3z=1 ....(ii)
−x−y−2z=0 ...(iii)
On solving Eqs. (i), (ii) and (iii), we get
x=
2
−3
,y=
2
1
z=
2
1
∴l=
c
3
hG
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