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Q.

A physical quantity of the dimensions of length that can be formed out of c, G and e24πε0c  is velocity of light, G is universal constant of gravitation and e is charge]

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a

c2Ge24πε01/2

b

1c2e2G4πε01/2

c

1cGe24πε0

d

1c2Ge24πε01/2

answer is D.

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Detailed Solution

Dimensions of e24πεo=F×d2=ML3 T-2 Dimensions of G=M-1L3T-2 Dimensions of c=LT-1l∝e24πεopGqcr∴  L1=ML3 T-2pM-1 L3 T-2qLT-1rOn comparing both sides and solving, we get p=12,  q=12 and r=-2∴l=1c2Ge24πεo1/2
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A physical quantity of the dimensions of length that can be formed out of c, G and e24πε0c  is velocity of light, G is universal constant of gravitation and e is charge]