Questions
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:
detailed solution
Correct option is A
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−5/2Talk to our academic expert!
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The quantities A and B are related by the relation A/B = m, where m is the linear mass density and A is the force, the dimensions of B will be
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