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Q.

Suppose you design your system of dimensions and take velocity(v), Planck's constant (h) and gravitational constant (G) as the fundamental quantities. What will be the dimensions of length(L) in this system.

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a

v3/2h1/2G1/2

b

v3/2h1/2G1/2

c

v3/2h1/2G1/2

d

v3/2h1/2G1/2

answer is D.

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Detailed Solution

We Know

[V]=LT1;[h]=ML2T1;

[G]=M1L3T2

 Let L=VahbGC

M0L1T0=LT1aML2T1bM1L3T2c

Comparing the powers of M, L, T both sides

b-c=0 – (1), a+2b+3c=1 – (2) ;

-a-b-2c=0 - (3)

On solving (1), (2) & (3)

We get a=3/2, b=1/2, c=1/2

L=V32h12G12

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