SATHEE: Physics And Measurement Question 123

Physics And Measurement Question 123

Question: If the speed of light $(c)$ , acceleration due to gravity $(g)$ and pressure $(p)$ are taken as the fundamental quantities, then the dimension of gravitational constant is

[AMU (Med.) 1999]

Options:

A) $c^{2} g^{0} p^{- 2}$

B) $c^{0} g^{2} p^{- 1}$

C) $c g^{3} p^{- 2}$

D) $c^{- 1} g^{0} p^{- 1}$

Show Answer

Answer:

Correct Answer: B

Solution:

Let $[G] \propto c^{x} g^{y} p^{z}$

by substituting the following dimensions :

$[G] = [M^{- 1} L^{3} T^{- 2}], [c] = [L T^{- 1}], [g] = [L T^{- 2}]$

$[p] = [M L^{- 1} T^{- 2}]$

and by comparing the powers of both sides

we can get $x = 0, y = 2, z = - 1$

$M L^{2} T^{- 2}$

$[G] \propto c^{0} g^{2} p^{- 1}$

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Physics And Measurement Question 123

Question: If the speed of light (c) , acceleration due to gravity (g) and pressure (p) are taken as the fundamental quantities, then the dimension of gravitational constant is

Options:

Answer:

Solution:

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Question: If the speed of light $(c)$ , acceleration due to gravity $(g)$ and pressure $(p)$ are taken as the fundamental quantities, then the dimension of gravitational constant is