SATHEE: Physics And Measurement Question 32

Physics And Measurement Question 32

Question: The speed of light $(c)$ , gravitational constant $(G)$ and Planck’s constant $(h)$ are taken as the fundamental units in a system. The dimension of time in this new system should be

[AMU 1995]

Options:

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

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

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

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

Show Answer

Answer:

Correct Answer: A

Solution:

Time $\propto c^{x} G^{y} h^{z} \Rightarrow T = k c^{x} G^{y} h^{z}$

Putting the dimensions in the above relation

$\Rightarrow$ $[M^{0} L^{0} T^{1}] = {[L T^{- 1}]}^{x} {[M^{- 1} L^{3} T^{- 2}]}^{y} {[M L^{2} T^{- 1}]}^{z}$

$\Rightarrow$ $[M^{0} L^{0} T^{1}] = [M^{- y + z} L^{x + 3 y + 2 z} T^{- x - 2 y - z}]$ Comparing the powers of $M, L$ and $T$

$- y + z = 0$ -(i)

$x + 3 y + 2 z = 0$ -(ii)

$- x - 2 y - z = 1$ -(iii)

On solving equations (i) and (ii) and (iii) $x = \frac{- 5}{2}, y = z = \frac{1}{2}$

Hence dimension of time are $[G^{1 / 2} h^{1 / 2} c^{- 5 / 2}]$

Physics And Measurement Question 32

Question: The speed of light $(c)$ , gravitational constant $(G)$ and Planck’s constant $(h)$ are taken as the fundamental units in a system. The dimension of time in this new system should be

Options:

Answer:

Solution:

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Physics And Measurement Question 32

Question: The speed of light (c) , gravitational constant (G) and Planck’s constant (h) are taken as the fundamental units in a system. The dimension of time in this new system should be

Options:

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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Question: The speed of light $(c)$ , gravitational constant $(G)$ and Planck’s constant $(h)$ are taken as the fundamental units in a system. The dimension of time in this new system should be