If the speed of light (c), acceleration due to gravity (g) and pressur

1.	If the speed of light (c), acceleration due to gravity (g) and pressure (p) are taken as the fundamental quantities, then the dimension of gravitational constant is (A) [c2 g0 p-2] (B) [c0 g2 p-1] (C) [cg3 p-2] (D) [c-1g0 p-1]
Answer» Answer is (B) [c⁰ g² p^-1] Let G ∝ c^xg^y p^z Substituting dimensions, [M^-1 L³ T^-2]= [M⁰L¹T^-1]^x [M⁰L¹T^-2] y [M¹ L^-1 T^-2]^z Comparing powers of M, L, T - 1 = z, x + y - z = 3 and - x - 2y - 2z = - 2 Solving, x = 0, y = 2

If the speed of light (c), acceleration due to gravity (g) and pressure (p) are taken as the fundamental quantities, then the dimension of gravitational constant is (A) [c2 g0 p-2] (B) [c0 g2 p-1] (C) [cg3 p-2] (D) [c-1g0 p-1]

Answer»

Answer is (B) [c⁰ g² p^-1]

Let G ∝ c^xg^y p^z

Substituting dimensions,

[M^-1 L³ T^-2]= [M⁰L¹T^-1]^x [M⁰L¹T^-2] y [M¹ L^-1 T^-2]^z

Comparing powers of M, L, T

- 1 = z,

x + y - z = 3 and

- x - 2y - 2z = - 2

Solving, x = 0, y = 2

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If the speed of light (c), acceleration due to gravity (g) and pressure (p) are taken as the fundamental quantities, then the dimension of gravitational constant is (A) [c2 g0 p-2] (B) [c0 g2 p-1] (C) [cg3 p-2] (D) [c-1g0 p-1]

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