Which of the following is the correct dimension for pressure? (2021)

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Question: Which of the following is the correct dimension for pressure? (2021)

Options:

Correct Answer: M^1L^-1T^-2

Exam Year: 2021

Solution:

Pressure is defined as force per unit area, hence its dimension is M^1L^-1T^-2.

Which of the following is the correct dimension for pressure? (2021)

Which of the following is the correct dimension for pressure? (2021)

Step 1: Understand that pressure is defined as the amount of force applied over a certain area.
Step 2: Recall the formula for pressure: Pressure = Force / Area.
Step 3: Identify the dimensions of force. Force is mass times acceleration (F = m * a).
Step 4: The dimension of mass (m) is M (mass).
Step 5: The dimension of acceleration (a) is change in velocity over time, which is L/T^2 (length per time squared).
Step 6: Therefore, the dimension of force (F) is M * (L/T^2) = M^1L^1T^-2.
Step 7: Now, consider the area. The dimension of area is length squared, which is L^2.
Step 8: Substitute the dimensions into the pressure formula: Pressure = (M^1L^1T^-2) / (L^2).
Step 9: Simplify the expression: M^1L^1T^-2 / L^2 = M^1L^(1-2)T^-2 = M^1L^-1T^-2.
Step 10: Conclude that the correct dimension for pressure is M^1L^-1T^-2.

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