Question

The force 'F' acting on a body of density 'd' are related by the relation F = `"y"/sqrt"d"`. The dimensions of 'y' are ______.

Options

• `["L"^(- 1/2) "M"^(3/2) "T"^-2]`

• `["L"^-1 "M"^(1/2) "T"^-2]`

• `["L"^(-1) "M"^(3/2) "T"^-2]`

• `["L"^(- 1/2) "M"^(1/2) "T"^-2]`

Answer 1

The force 'F' acting on a body of density 'd' are related by the relation F = `"y"/sqrt"d"`. The dimensions of 'y' are `underline(["L"^(- 1/2) "M"^(3/2) "T"^-2])`.

Explanation:

The dimensions of force [F] = [MLT^-2]

and density [d] = [ML³ T⁰]

From the given relation, F = `"y"/sqrt"d"`

⇒ y = F`sqrt"d"`

Substituting the above dimensions, we get

[y] = [F][d]^1/2 = [ML T^-2][ML^-3 T⁰]^1/2

= [M^3/2 L^-1/2 T^-2]