Question

A physical quantity X is defined by the formula 

\(X =\dfrac{IFv^2}{WL^3}\)

where I is moment of inertia, F is force, v is velocity, W is work and L is length, the dimensions of X are:

1. MLT^-2
2. MT^-2
3. M²T^-3
4. LT^-1

Answer 1

Correct Answer - Option 2 : MT^-2

CONCEPT:

• Dimensional formula: It is a compound expression showing how and which of the fundamental quantities are involved in making that physical quantity.

Quantity	Dimensional formula
Force (F)	[MLT-2]
velocity (v)	[LT-1]
Inertia (I)	[M1L2T3]
Surface tension (S)	[ML0T-2]
Spring constant (K)	[ML0T-2]
Length	[L]
Work (W)	[ML2T-2]
Any constant (C)	No dimension

CALCULATION:

Given quantity \(X =\dfrac{IFv^2}{WL^3}\)

Take dimensions of both sides

\([X] =\dfrac{[I][F][v^2]}{[W][L^3]}\)

\([X] =\dfrac{[M^1L^2T^3][MLT^{-2}][LT^{-1}]^2}{[ML^2T^{-2}][L^3]}\)

\([X] =[MT^{-2}]\)

• So the correct answer is option 2.