Question

If E, L, M, and G denote the quantities as energy, angular momentum, mass, and constant of gravitation respectively, then the dimensions of P in the formula P = EL²M^-5G^-2 are ______.

विकल्प

• [M⁰L¹T⁰]

• [M^-1L^-1T²]

• [M⁰L⁰T⁰]

• [M¹L¹T^-2]

Answer 1

If E, L, M, and G denote the quantities as energy, angular momentum, mass, and constant of gravitation respectively, then the dimensions of P in the formula P = EL²M^-5G^-2 are [M⁰L⁰T⁰].

Explanation:

since

The dimensions of energy [E] = [ML²T^-2]

The dimensions of angular momentum [L] = [ML²T^-1]

The dimensions of mass [M] = [M]

The dimensions of gravitational constant [G] = [M^-1L³T^-2]

Given, P = EL²M^-5G^-2

Hence, P's dimensions will be

[P] = [ML²T^-2][ML²T^-1]²[M]^-5[M^-1L³T^-2]^-2

= [ML²T^-2][M²L⁴T^-2][M^-5][M²L^-6T⁴]

= [M⁰L⁰T⁰]