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Q.

The dimension of stopping potential V0  in photoelectric effect in units of Planck’s constant ‘h’, speed of light ‘C’ and universal gravitational constant ‘G’ and ampere A is:

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a

h1/3G2/3,C1/3A1

b

h0 , C5, G-1, A1

c

h2/3,C1/3,G4/3,A1

d

h2 , G3/2, C1/3 , A1

answer is B.

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Detailed Solution

V=KhaAbGcCd  (V is voltage)
We know  h=ML2T1
[A] = A
[G] = M-1L3T-2
[C] = LT-1
[V] =   ML2T-3A1
  

comparing dimensions on both sides,

 ML2T-3A1  =   ML2T1aAbM1L3T2cLT1d
 ⇒ML2T-3A1  =  MacL2a+3c+dTa2cdAb

Comparing the powers, 
 ac=1..................(1)
b=1.................2

a2cd = 3 .........32a+3c+d = 2 .............4

Add 3 and 4 ,  a+c = 1 .........5Add 1 and 5 , 2a =0a=0c=1Put values of a and c in 3,2d=3d=5​​Thus, V=K h0A1G1C5

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