Published by:
CGP EDU Academic Team
Published on: September 12, 2026
The expression \(\left[ML^{\frac{2}{7}} \cdot T^{-\frac{2}{7}}\right]\) represents
Text Solution
Verified by ExpertsThe correct answer is:
A
To determine what the expression \([ML^{-1}T^{-2}]\) represents, we can analyze its dimensional formula:
Now, we break down the expression:
1. The unit \([M]\) indicates mass.
2. The unit \([L^{-1}]") indicates that it is divided by length, which is a characteristic of pressure (force per unit area).
3. The unit \([T^{-2}]\) indicates an inverse square relationship with time, which is typical in dynamics.
Combining these components, we recognize that the expression \([ML^{-1}T^{-2}]\) corresponds to pressure (force per unit area) as pressure is defined as \(P = \frac{F}{A} = \frac{[M][L][T^{-2}]}{[L^{2}]} = [ML^{-1}T^{-2}]\). Therefore, the correct answer is Option A: Pressure.
- [M] stands for mass (in kilograms).
- [L] stands for length (in meters).
- [T] stands for time (in seconds).
Now, we break down the expression:
1. The unit \([M]\) indicates mass.
2. The unit \([L^{-1}]") indicates that it is divided by length, which is a characteristic of pressure (force per unit area).
3. The unit \([T^{-2}]\) indicates an inverse square relationship with time, which is typical in dynamics.
Combining these components, we recognize that the expression \([ML^{-1}T^{-2}]\) corresponds to pressure (force per unit area) as pressure is defined as \(P = \frac{F}{A} = \frac{[M][L][T^{-2}]}{[L^{2}]} = [ML^{-1}T^{-2}]\). Therefore, the correct answer is Option A: Pressure.
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