📘 Numerical Problems (Mechanical Properties of Matter)
Master the Numerical Problems of Chapter 6 – Mechanical Properties of Matter from Class 9 Physics with step-by-step solutions. This resource covers essential calculations including spring constant, density, pressure, hydraulic systems, and fluid pressure, aligned with the Punjab PECTA 2025 syllabus. Practice problems on Hooke's law, hydraulic press applications, and pressure at depth with detailed explanations.
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Important Formulas
Key Formulas for Numerical Problems
Density
\[\rho = \frac{m}{V}\]Where \( \rho \) is density, \( m \) is mass, and \( V \) is volume
Pressure
\[P = \frac{F}{A}\]Where \( P \) is pressure, \( F \) is force, and \( A \) is area
Spring Constant (Hooke's Law)
\[k = \frac{F}{x}\]Where \( k \) is spring constant, \( F \) is force, and \( x \) is extension
Hydraulic Press Equation
\[\frac{F_1}{A_1} = \frac{F_2}{A_2}\]Where \( F_1 \) and \( F_2 \) are forces, \( A_1 \) and \( A_2 \) are areas
Pressure at Depth in Liquid
\[P = \rho g h\]Where \( P \) is pressure, \( \rho \) is density, \( g \) is gravity, and \( h \) is depth
Problem Categories
Hooke's Law and Spring Constant Problems
These problems involve calculating spring constant, force, or extension using Hooke's law:
- Finding spring constant from force and extension
- Calculating force for a given extension
- Determining extension for a given force
Density Problems
These problems involve calculating density, mass, or volume:
- Finding density from mass and volume
- Calculating mass from density and volume
- Determining volume from mass and density
- Using displacement method for irregular solids
Pressure Problems
These problems involve calculating pressure, force, or area:
- Finding pressure from force and area
- Calculating force from pressure and area
- Determining area from force and pressure
- Maximum and minimum pressure for objects with different orientations
Hydraulic Systems Problems
These problems involve Pascal's law and hydraulic systems:
- Calculating force multiplication in hydraulic presses
- Finding pressure in hydraulic brake systems
- Determining forces on different pistons
Atmospheric Pressure Problems
These problems involve calculations related to atmospheric pressure:
- Finding height of liquid columns in barometers
- Calculating pressure at different depths in liquids
- Pressure variations with altitude
Problem-Solving Strategies
Follow these steps for solving numerical problems effectively:
1. Understand the Problem
- Read the problem carefully and identify what is being asked
- Note down all given quantities with their units
- Identify the unknown quantity to be found
2. Select the Appropriate Formula
- Choose the formula that relates the given and unknown quantities
- Ensure you understand what each variable in the formula represents
- Check if any rearrangements of the formula are needed
3. Convert Units
- Convert all quantities to SI units before calculations
- Pay special attention to:
- Length: cm to m (1 cm = 0.01 m)
- Area: cm² to m² (1 cm² = 0.0001 m²)
- Volume: cm³ to m³ (1 cm³ = 0.000001 m³)
- Mass: g to kg (1 g = 0.001 kg)
4. Perform Calculations
- Substitute the values into the formula
- Perform the calculations step by step
- Keep track of units throughout the calculation
5. Check Your Answer
- Ensure the answer has the correct units
- Verify that the magnitude of the answer is reasonable
- Check if the answer makes physical sense
Unit Conversion Guide
Practice Tips
Effective Practice Strategies
- Start with basic problems: Begin with simple calculations to build confidence
- Focus on unit conversions: Many errors occur due to incorrect unit conversions
- Practice regularly: Consistent practice helps reinforce concepts
- Review mistakes: Analyze errors to understand where you went wrong
- Time yourself: Practice solving problems within time limits
- Create formula sheets: Make personalized formula summaries for quick reference
Created by Hira Science Academy | Aligned with PECTA 2025 Syllabus