JEE MainPhysicsUnits and Dimensions
The velocity v of a small particle in a viscous medium is given by the relation v = ( ) ( x ) , where x is the distance and is the coefficient of viscosity of the medium. If and are constants, the dimensions of will be
Options
- A[ M L ^2 T ⁻³ ]
- B[ M T ⁻² ]
- C[ M L ⁻² T ⁻¹ ]
- D[ M L ⁻¹ T ⁻² ]
Correct answer
D. [ M L ⁻¹ T ⁻² ]
Step-by-step solution
Given v = ( ) ( x ) The argument of a trigonometric function is dimensionless. Therefore, [ x ] = [ M ^0 L ^0 T ^0 ] [ ] = [ x ] The dimensional formula for the coefficient of viscosity is [ M L ⁻¹ T ⁻¹ ] and for distance x is [ L ] . [ ] = [ M L ⁻¹ T ⁻¹ ] [ L ] = [ M L ⁻² T ⁻¹ ] From the principle of homogeneity, the dimensions of the left-hand side must equal the dimensions of the right-hand side. [v] = [ ] [ ] = [v][ ] Since velocity v has dimensions [ L T ⁻¹ ] , we get: [ ] = [ L T ⁻¹ ] [ M L ⁻² T ⁻¹ ] = [ M L