Question

If the dimensions of a physical quantity are given by \( [L^{-1} M^0 T^1] \), then the physical quantity is

• A. velocity if \( a = -1, b = 0, c = +1 \)
• B. force if \( a = -1, b = 1, c = -2 \)
• C. pressure if \( a = -1, b = 1, c = -2 \)
• D. acceleration if \( a = 1, b = 1, c = -2 \)

Hint:

Always verify the dimensional formula for different quantities. The dimensions of pressure are \( [M L^{-1} T^{-2}] \).

Answer 1

The Correct Option is C

Step 1: Understanding the dimensions.
The dimensional formula is given by \( [L^{-1} M^0 T^1] \). This represents a physical quantity with the dimension of length raised to the power of -1, mass raised to the power of 0 (indicating mass is not involved), and time raised to the power of 1.

Step 2: Identifying the correct physical quantity.
- For velocity, the dimensions are \( [L^1 T^{-1}] \), which do not match. - For force, the dimensions are \( [M L T^{-2}] \), which do not match. - For pressure, the dimensions are \( [M L^{-1} T^{-2}] \), which match the given formula. - For acceleration, the dimensions are \( [L T^{-2}] \), which also do not match.

Step 3: Conclusion.
The physical quantity corresponding to \( [L^{-1} M^0 T^1] \) is pressure. Thus, the correct answer is (C).