Manipal MET2021PhysicsUnits and Dimensions
The displacement of an oscillating particle is given by y=A [B x+C t+D t] . The dimensional formula for [A B C D] is :
Options
- A[ M ^0 ~L ⁻¹ ~T ^0 ]
- B[ M ^0 ~L ^0 ~T ⁻¹ ]
- C[ M ^ L ⁻¹ ~T ⁻¹ ]
- D[M^0 L^0 T^0 ]
Correct answer
B. [ M ^0 ~L ^0 ~T ⁻¹ ]
Step-by-step solution
y=A [B x+C t+D] As each term inside the bracket is dimension less, [A]=[y]=[L], [B]= 1 [x] = [L⁻¹ ] [C]= 1 [t] = [1⁻¹ ] and D is dimensionless. [A B C D]=[ L ] [ L ⁻¹ ] [ T ⁻¹ ][1]= [ N ^0 ~L ^0 ~T ⁻¹ ]