Key Formulas: Work-Energy, Motion, and Thermodynamics Explained
FAQs on Essential Physics Relations for Classes 11 & 12 – Free PDF
1. What is the fundamental relation between work and energy in physics?
The fundamental relationship is defined by the work-energy theorem, which states that the net work done on an object is equal to the change in its kinetic energy. Essentially, work is the mechanism for transferring energy. If positive work is done, the object's kinetic energy increases; if negative work is done, it decreases. The SI unit for both work and energy is the Joule.
2. How are velocity and acceleration related?
Acceleration is defined as the rate of change of velocity over time. Since velocity is a vector quantity (possessing both magnitude and direction), an object is considered to be accelerating if its speed changes, its direction of motion changes, or both change simultaneously. The relation is mathematically expressed as a = Δv / Δt.
3. What is the relation between force, mass, and acceleration as described by Newton's Second Law?
Newton's Second Law of Motion establishes a core relationship in mechanics: the net force (F) acting on an object is directly proportional to its acceleration (a) and equal to the product of its mass (m) and acceleration. The formula is F = ma. This implies that a greater force is required to achieve the same acceleration for an object with a larger mass.
4. How does the relationship between electric current, voltage, and resistance (Ohm's Law) apply in everyday electronic devices?
Ohm's Law, given by V = IR, is the foundational principle for nearly all electronic circuits. In everyday devices, this relation is used to control and manage electricity. For example:
- In a phone charger, resistors are used to control the amount of current (I) flowing to the battery, preventing overcharging and damage.
- In an electric heater, a high-resistance wire is used so that when voltage (V) is applied, it generates a large amount of heat (as per Joule's law of heating, which is derived from this relation).
5. What is the thermodynamic relation between specific heat at constant pressure (Cp) and constant volume (Cv)?
The relation between the molar specific heat at constant pressure (Cₚ) and at constant volume (Cᵥ) for an ideal gas is described by Mayer's relation: Cₚ – Cᵥ = R, where R is the universal gas constant. The value of Cₚ is always greater than Cᵥ because when a gas is heated at constant pressure, it must expand and perform work, thus requiring more heat energy to achieve the same temperature rise compared to when it is heated at a constant volume.
6. Why is Einstein's mass-energy equivalence relation, E=mc², considered a cornerstone of modern physics?
The relation E=mc² is revolutionary because it demonstrates that mass and energy are two forms of the same thing and are interchangeable. It is not merely that mass possesses energy, but that mass itself is a highly concentrated form of energy. This principle is a cornerstone because it explains phenomena that classical physics could not, such as:
- Nuclear Energy: How nuclear reactors and atomic bombs release immense energy by converting a tiny fraction of mass.
- Stellar Fusion: How stars, including our Sun, generate light and heat by fusing light nuclei into heavier ones, converting mass into energy.
- Particle Physics: How energy can be converted into particles with mass in high-energy accelerators.
7. What is the key difference between the physical relations for momentum and kinetic energy?
While both momentum and kinetic energy relate to an object's mass and velocity, they describe fundamentally different physical concepts:
- Momentum (p = mv) is a vector quantity that measures an object's 'quantity of motion' and has a direction. It is always conserved in a closed system.
- Kinetic Energy (KE = ½mv²) is a scalar quantity that measures the energy an object possesses due to its motion. It has no direction and is only conserved in perfectly elastic collisions.
8. How are frequency, wavelength, and the speed of a wave related?
For any wave, the relationship between its speed (v), frequency (f), and wavelength (λ) is given by the universal wave equation: v = fλ. This means the speed of a wave is the product of its frequency (number of oscillations per second) and its wavelength (the spatial period of the wave). For electromagnetic waves like light traveling in a vacuum, the speed 'v' is a constant 'c'. Therefore, their frequency and wavelength are inversely proportional; a wave with a high frequency will have a short wavelength, and vice versa.
