NEETPhysicsUnits and Dimensions
A force F varies with distance x and time t according to the equation F = A (Bx) + C (Dt) . The dimensional formula of the ratio A D C B is:
Options
- A[M^0 L^1 T⁻¹]
- B[M^0 L^0 T^0]
- C[M^0 L⁻¹ T^1]
- D[M^0 L⁻¹ T⁻¹]
Correct answer
A. [M^0 L^1 T⁻¹]
Step-by-step solution
By the principle of homogeneity, the dimensions of each term added together must be the same as the dimensions of the LHS. Therefore, [A] = [F] and [C] = [F] . This implies that the ratio A C is dimensionless, i.e., [ A C ] = [M^0 L^0 T^0] . The arguments of trigonometric functions must be dimensionless. For (Bx) , the argument Bx is dimensionless: [B] [x] = [M^0 L^0 T^0] [B] [L] = 1 [B] = [L⁻¹] For (Dt) , the argument Dt is dimensionless: [D] [t] = [M^0 L^0 T^0] [D] [T] = 1 [D] = [T⁻¹] Now, finding the dimensions