Final answer:
The assertion that Lˉ has the dimensions of time is false because L represents length, not time. The correct answer is (d) Both the assertion and the reason are false. The correct answer (d) Both the assertion and the reason are false.
Step-by-step explanation:
The question asserts that the quantity Lˉ has the dimensions of time. To evaluate this assertion, we need to consider what is known about dimensions in physics.
The dimensions of physical quantities are expressed by an algebraic combination of the base quantities: length (L), mass (M), time (T), electric current (I), thermodynamic temperature (Θ), amount of substance (N), and luminous intensity (J).
Speed is an example of a physical quantity with dimensions, specifically as L/T or LT⁻¹. The assertion suggests that Lˉ possesses the dimensions of time, which is incorrect as L represents length, and time is represented by T.
Therefore, the assertion is false. The reason provided in the question is incomplete and does not give enough context to accurately determine its truth or relevance. Accordingly, the response that both the assertion and the reason are false is suitable, making the correct answer (d) Both the assertion and the reason are false.