Question

The dimensions of pressure are same as that of: (a) Energy (b) Energy per unit volume (c) Force per unit area (d) Force per unit volume

Short answer

Both (b) Energy per unit volume and (c) Force per unit area have the same dimensions as pressure, \([M L^{-1} T^{-2}]\).

Step-by-step solution

Recall the definition of pressure

Pressure is defined as force per unit area. Mathematically, it is expressed as \( P = \frac{F}{A} \), where \( P \) represents pressure, \( F \) is the force applied, and \( A \) is the area over which the force is distributed.

Determine the dimensions of pressure

Using the formula for pressure \( P = \frac{F}{A} \), we know the dimension of force \( F \) is \( [M L T^{-2}] \) and the dimension of area \( A \) is \( [L^2] \). Thus, the dimension of pressure is calculated as \( [M L T^{-2}] \times [L^{-2}] = [M L^{-1} T^{-2}] \).

Compare with the given options

The given options are dimensions related to (a) Energy, (b) Energy per unit volume, (c) Force per unit area, (d) Force per unit volume. Let's match these with our derived pressure dimensions:- Energy has dimensions \( [M L^2 T^{-2}] \).- Energy per unit volume has dimensions \( [M L^{-1} T^{-2}] \).- Force per unit area is same as pressure by definition \( [M L^{-1} T^{-2}] \).- Force per unit volume has dimensions \( [M L^{-2} T^{-2}] \).Option (b) Energy per unit volume and (c) Force per unit area both match the dimensions of pressure.

Key concepts

SI Units of Pressure

Pressure is an essential concept in physics that describes how force is distributed over an area. The standard unit of pressure in the International System of Units (SI) is the pascal (Pa). One pascal is equal to one newton per square meter, and it serves as the foundation for measuring pressure. The formula for pressure, expressed as \( P = \frac{F}{A} \), shows its derivation from force (newtons) and area (square meters).
Understanding the SI unit enables a global consistency in measuring and interpreting pressure values, crucial in fields like engineering, meteorology, and medicine. Other pressure units include the bar, atmosphere (atm), and millimeters of mercury (mmHg), but they are often converted to pascals for standardization.
It's also important to recognize how uniform pressure units help standardize calculations and experiments, making comparisons and solutions truly universal.

Dimensional Analysis

Dimensional analysis is a method used in physics to understand the nature of physical quantities and equations. By breaking down an equation into basic dimensions (mass \(M\), length \(L\), and time \(T\)), one can verify its correctness and understand the relationships between different quantities.
For pressure, using the formula \( P = \frac{F}{A} \), we start by identifying the dimensions of force \(F\) (\([M L T^{-2}]\)) and area \(A\) (\([L^2]\)). When we substitute these into the pressure formula, we obtain the dimensions \([M L^{-1} T^{-2}]\).
This analysis helps in identifying pressure's relationship with other quantities, confirming that pressure shares dimensions with energy per unit volume and force per unit area. Mastering dimensional analysis aids in verifying that physics equations are dimensionally consistent, which is crucial for solving complex problems accurately.

Pressure Calculation

Calculating pressure involves understanding how a force is distributed over an area. The concept is fundamental in physics as it determines how energy or force affects a surface.
The formula \( P = \frac{F}{A} \) allows us to compute pressure when given the force and area. Consider a force of 10 newtons applied over an area of 2 square meters. The pressure would be calculated as \( 5 \text{ Pa} \) (pascals).
Understanding this calculation enables practical applications, like determining how tire pressure affects vehicle performance or how atmospheric pressure influences weather systems. Accurate pressure calculation is key in designing safe structures and efficient systems across various industries.
Students often practice pressure calculation to strengthen their problem-solving skills, laying a foundation for more advanced physics concepts.

Physics Problem Solving

Problem-solving in physics requires a structured approach to apply theoretical concepts to practical situations. This process often begins with understanding the problem, identifying known and unknown variables, and selecting the appropriate equations.
For pressure-related problems, identifying forces and areas is vital. After determining these values, applying the formula \( P = \frac{F}{A} \) allows for pressure calculation. Analyzing results and considering their implications reveals the problem's broader significance, whether in understanding mechanical systems or predicting natural phenomena.
Physics problem-solving encourages critical thinking and logical reasoning.
To enhance these skills, students should:

• Break complex problems into smaller, more manageable parts.
• Regularly practice solving diverse problems to build familiarity with different scenarios.
• Collaborate with peers to exchange ideas and techniques.

Through consistent practice and application of these strategies, solving physics problems becomes more intuitive and rewarding.