SATHEE: Physics And Measurement Question 138

Physics And Measurement Question 138

Question: If the velocity of light $(c)$ , gravitational constant $(G)$ and Planck’s constant $(h)$ are chosen as fundamental units, then the dimensions of mass in new system is

[UPSEAT 2002]

Options:

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

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

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

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

Show Answer

Answer:

Correct Answer: C

Solution:

Let $m \propto C^{x} G^{y} h^{z}$

By substituting the following dimensions: $[C] = L T^{- 1}; [G] = [M^{- 1} L^{3} T^{- 2}]$

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

Now comparing both sides we will get

$x = 1 / 2; y = - 1 / 2, z = + 1 / 2$ So $m \propto c^{1 / 2} G^{- 1 / 2} h^{1 / 2}$

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Physics And Measurement Question 138

Question: If the velocity of light (c) , gravitational constant (G) and Planck’s constant (h) are chosen as fundamental units, then the dimensions of mass in new system is

Options:

Answer:

Solution:

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Question: If the velocity of light $(c)$ , gravitational constant $(G)$ and Planck’s constant $(h)$ are chosen as fundamental units, then the dimensions of mass in new system is