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Q.

The speed of light(c), gravitational constant (G) and Plank’s constant (h) are taken as

            fundamental units in a system. The dimensions of time in this new system should be

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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

we have cxGyhz kcxGyhz According to the method of dimensional analysis  the dimension of each term on both sides of    an equation must be same.  Putting the dimensional formula in above relation M0L0T1=LT1xM1L3T2yML2T1z M0L0T1=My+zLx+3y+2zTx2yz Comparing the dimensions of M, L and T y+z=0i x+3y+2z=0ii x2yz=1iii On solving equations (i), (ii) and (iii) x=52  ,  y=z=12 Hence, dimensions of time are G1/2h1/2c5/2

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