Question

13. Which of the following quantities has the same dimensions as the gravitational constant?
(a) (Velocity)?/mass per unit length
(b) Force/mass
(C) (Momentum)?/force
(d) work/time
Amandada​

Answer 1

Answer:

Explanation:

Option C is correct Please mark me as brainlist

Answer 2

Concept:

Dimensional formulas are the formulas that are written using the seven fundamental physical quantities.

Given:

A physical quantity, gravitational constant.

Find:

The one has a dimension the same as the gravitational constant.

Solution:

Dimension of gravitational constant,

G = Fr²/(Mm)

where F is the force, r is the distance, and M, and m are the masses.

So, the dimension of gravitational constant is,

G = [M⁻¹L³T⁻²]

Similarly, the Dimension of Velocity²/mass per unit length,

D₁ = v²/(m/l)

D₁ = [M⁻¹L³T⁻²]

Similarly, the Dimension of Force/mass,

D₂ = F/m

D₂ = [L¹T⁻²]

Similarly, the Dimension of (Momentum)²/force

D₃ = p²/F

D₃ = [M¹L¹]

Similarly, the Dimension of work/time

D₄ = W/t = Energy

D₄ = [M¹L²T⁻²]

Hence, the dimensional formula of gravitational constant and Velocity²/mass per unit length is the same. Hence, the correct option is (a) Velocity²/mass per unit length.

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