Question

A quantity x is by (IFv²/WL⁴) in term of moment of inertia I, force F, velocity v, work W and Length L. The dimensional formula for x is same as that of ______.

Options

• Planck's constant

• force constant 

• coefficient of viscosity

• energy density

Answer 1

A quantity x is by (IFv²/WL⁴) in term of moment of inertia I, force F, velocity v, work W and Length L. The dimensional formula for x is same as that of energy density.

Explanation:

Dimension of Force F = M¹L¹T^--2

Dimension of velocity V= L¹T^-1

Dimension of work = M¹L²T^-2

Dimension of length = L

Moment of inertia = ML²

∴ x = `"IFv"^2/"WL"^4 = (("M"^1"L"^2)("M"^1"L"^1"T"^-2)("L"^1"T"^-2)^2)/(("M"^1"L"^2"T"^-2)("L"^4))`

= `("M"^1"L"^-2"T"^-2)/"L"^3`

= M¹L^-1T^-2 = Energy density