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

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

$G^{1 / 2} h^{1 / 2} c^{- 5 / 2}$

$G^{- 1 / 2} h^{1 / 2} c^{1 / 2}$

$G^{1 / 2} h^{1 / 2} c^{- 3 / 2}$

$G^{1 / 2} h^{1 / 2} c^{1 / 2}$

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$w e h a v e \propto c^{x} G^{y} h^{z} \Rightarrow k c^{x} G^{y} h^{z} A c c o r d i n g t o t h e m e t h o d o f d i m e n s i o n a l a n a l y s i s t h e d i m e n s i o n o f e a c h t e r m o n b o t h s i d e s o f a n e q u a t i o n m u s t b e s a m e . P u t t i n g t h e d i m e n s i o n a l f o r m u l a i n a b o v e r e l a t i o n \Rightarrow [M^{0} L^{0} T^{1}] = {[L T^{- 1}]}^{x} {[M^{- 1} L^{3} T^{- 2}]}^{y} {[M L^{2} T^{- 1}]}^{z} \Rightarrow [M^{0} L^{0} T^{1}] = [M^{- y + z} L^{x + 3 y + 2 z} T^{- x - 2 y - z}] C o m p a r i n g t h e d i m e n s i o n s o f M, L a n d T - y + z = 0 \to (i) x + 3 y + 2 z = 0 \to (i i) - x - 2 y - z = 1 \to (i i i) O n s o l v i n g e q u a t i o n s (i), (i i) a n d (i i i) x = \frac{- 5}{2}, y = z = \frac{1}{2} H e n c e, d i m e n s i o n s o f t i m e a r e [G^{1 / 2} h^{1 / 2} c^{- 5 / 2}]$