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Standard XII

Physics

Dimensional Analysis

If the speed ...

Question

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

c^{2} g^{0} p^{- 2}

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c^{0} g^{2} p^{- 1}

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c g^{3} p^{- 2}

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c^{- 1} g^{0} p^{- 1}

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Solution

The correct option is A $c^{0} g^{2} p^{- 1}$
Let $[G] \propto c^{x} g^{y} p^{z}$

by substituting the following dimension ;
$[G] = [M^{- 1} L^{3} T^{- 2}], [c] = [L T^{- 1}], [g] = [L T^{- 2}]$

and by comparing the power of both the sides
we can get $x = 0, y = 2, z = - 1$

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

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

The correct option is A c0g2p−1Let [G]∝cxgypzby substituting the following dimension ;[G]=[M−1L3T−2],[c]=[LT−1],[g]=[LT−2]and by comparing the power of both the sideswe can get x=0,y=2,z=−1So,[G]∝c0g2p−1