SATHEE: Physics And Measurement Question 29

Physics And Measurement Question 29

Question: If the dimensions of length are expressed as $G^{x} c^{y} h^{z}$ ; where $G, c$ and $h$ are the universal gravitational constant, speed of light and Planck’s constant respectively, then

[IIT 1992]

Options:

A) $x = \frac{1}{2}, y = \frac{1}{2}$

B) $x = \frac{1}{2}, z = \frac{1}{2}$

C) $y = \frac{1}{2}, z = \frac{3}{2}$

D) $y = - \frac{3}{2}, z = \frac{1}{2}$

Show Answer

Answer:

Correct Answer: B

Solution:

Length µ Gxcyhz L= ${[M^{- 1} L^{3} T^{- 2}]}^{x}$

${[L T^{- 1}]}^{y} {[M L^{2} T^{- 1}]}^{z}$

By comparing the power of M, L and T in both sides we get $- x + z = 0$ , $3 x + y + 2 z = 1$

and $- 2 x - y - z = 0$ By solving above three equations we get

$x = \frac{1}{2}, y = - \frac{3}{2}, z = \frac{1}{2}$

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Physics And Measurement Question 29

Question: If the dimensions of length are expressed as Gxcyhz ; where G,c and h are the universal gravitational constant, speed of light and Planck’s constant respectively, then

Options:

Answer:

Solution:

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Question: If the dimensions of length are expressed as $G^{x} c^{y} h^{z}$ ; where $G, c$ and $h$ are the universal gravitational constant, speed of light and Planck’s constant respectively, then