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 ______.

Options

• [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]