Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): In the relation x = (1 - e^ - t ) , where x is displacement and t is time, the dimensional formula of is [L T⁻¹] . Reason (R): The constant has the dimensional formula of [T] . In the light of the above statements, choose the most appropriate answer from the options given below:

Step-by-step solution

The exponent of an exponential function must be a dimensionless quantity. Therefore, the term t is dimensionless. [ ][t] = [M^0 L^0 T^0] [ ][T] = 1 [ ] = [T⁻¹] . Thus, the Reason (R) is false. According to the principle of homogeneity, the dimensions of the left-hand side must equal the dimensions of the right-hand side. The term (1 - e^ - t ) is a dimensionless number. [x] = [ ] [ ] [L] = [ ] [T⁻¹] [ ] = [L][T⁻¹] = [L T⁻¹] . Thus, the Assertion (A) is true. Therefore, Assertion (A) is true but Reason (R) is false.