Q.

The speed of light (c), gravitational constant (G) and Planck's constant (h) are taken as the fundamental units  in a system. The dimension of time in this system is:

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a

G1/2h1/2c5/2

b

G1/2h1/2c1/2

c

G1/2h1/2c1/2

d

G1/2h1/2c3/2

answer is A.

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Detailed Solution

 Time cxGyhzT=kcxGyhz

Putting the dimensions in the above relation

 M0L0T1=LT1xM1L3T2yML2T1z M0L0T1=M-y+zLx+3y+2zTx2yz

Comparing the powers of M, L and T

y+z=0        ...........(i)x+3y+2z=0 ...........(ii)x2yz=1 ..........(iii)

On solving equations (i) and (ii) and (iii)

x=52,y=z=12

Hence dimension of time are G1/2h1/2c5/2

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