SATHEE: Physics And Measurement Question 264

Physics And Measurement Question 264

Question: A physical quantity of the dimensions of length that can be formed out of c, G and $\frac{e^{2}}{4 π ε_{0}}$ is

[c is velocity of light, G is universal constant of gravitation and e is charge]

Options:

A) $c^{2} [G \frac{e^{2}}{4 π ε_{0}}]$

B) $\frac{1}{c^{2}} {[\frac{e^{2}}{G 4 π ε_{0}}]}^{1 / 2}$

C) $\frac{1}{c} G \frac{e^{2}}{4 π ε_{0}}$

D) $\frac{1}{c^{2}} {[G \frac{e^{2}}{4 π ε_{0}}]}^{1 / 2}$

Show Answer

Answer:

Correct Answer: D

Solution:

[d] Let dimensions of length is related as, $L = {[c]}^{x} {[G]}^{y} {[\frac{e^{2}}{4 π ε_{0}}]}^{z} \Rightarrow \frac{e^{2}}{4 π ε_{0}} = M L^{3} T^{- 2}$

$L = {[L T^{- 1}]}^{x} {[M^{- 1} L^{3} T^{- 2}]}^{y} {[M L^{3} T^{- 2}]}^{z}$

$[L] = [L^{x + 3 y + 3 z} M^{- y + z} T^{- x - 2 y - 2 z}]$

Comparing both sides $z = y = \frac{1}{2}, x = - 2$

Hence, L= $c^{- 2} {[G . \frac{e^{2}}{4 π ε_{0}}]}^{1 / 2}$

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Physics And Measurement Question 264

Question: A physical quantity of the dimensions of length that can be formed out of c, G and e24πε0 is

Options:

Answer:

Solution:

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Question: A physical quantity of the dimensions of length that can be formed out of c, G and $\frac{e^{2}}{4 π ε_{0}}$ is