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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

G1/2h1/2c−5/2

b

G−1/2h1/2c1/2

c

G1/2h1/2c−3/2

d

G1/2h1/2c1/2

answer is A.

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Detailed Solution

Time ∝cxGyhz⇒T=kcxGyhzPutting the dimensions in the above relation⇒ M0L0T1=LT−1xM−1L3T−2yML2T−1z⇒ M0L0T1=M-y+zLx+3y+2zT−x−2y−zComparing the powers of M, L and T−y+z=0        ...........(i)x+3y+2z=0 ...........(ii)−x−2y−z=1 ..........(iii)On solving equations (i) and (ii) and (iii)x=−52,y=z=12Hence dimension of time are G1/2h1/2c−5/2
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