Physics - 1 (Aut - 14, Sp - 13, Sp - 12, Sp - 15)

1. What is Surface Tension?

Answer:
Surface tension is the property of a liquid where its surface acts like a stretched elastic sheet. It is caused by cohesive forces between liquid molecules.

Derivation for Surface Tension Formula:
$T = \frac{F}{L}$
Where:

$T$ : Surface tension
$F$ : Force
$L$ : Length over which force acts

2. Derive Bernoulli’s Theorem

Answer:
Bernoulli's theorem states that for a fluid in steady flow, the sum of pressure energy, kinetic energy, and potential energy per unit volume is constant.

Derivation:
$\frac{P}{\rho} + \frac{v^2}{2} + gh = \text{constant}$
Where:

$P$ : Pressure
$\rho$ : Density
$v$ : Velocity
$g$ : Gravitational acceleration
$h$ : Height

This equation combines energy conservation principles.

3. What is Simple Harmonic Motion (SHM)?

Answer:
SHM is a type of oscillatory motion where an object moves back and forth about an equilibrium position, and its restoring force is proportional to displacement.

Equation of SHM:
$x = A \sin(\omega t + \phi)$
Where:

$A$ : Amplitude
$\omega$ : Angular frequency
$t$ : Time
$\phi$ : Phase constant

4. State and Explain the First Law of Thermodynamics

Answer:
The first law of thermodynamics states:
$\Delta Q = \Delta U + \Delta W$
Where:

$\Delta Q$ : Heat added to the system
$\Delta U$ : Change in internal energy
$\Delta W$ : Work done by the system

It explains energy conservation in thermal systems.

5. Define Diffraction Grating

Answer:
A diffraction grating is an optical device with many parallel lines that diffract light into different directions. It separates light into its component wavelengths.

6. What is Viscosity?

Answer:
Viscosity is the measure of a fluid's resistance to flow. It describes how thick or sticky a fluid is.

Formula:
The force due to viscosity is given by:
$F = \eta \cdot A \cdot \frac{v}{d}$
Where:

$F$ : Force due to viscosity
$\eta$ : Coefficient of viscosity
$A$ : Area of contact
$v$ : Velocity of fluid
$d$ : Distance between layers

7. Define Critical Velocity

Answer:
Critical velocity is the maximum velocity of a fluid flow in a pipe or channel before it changes from laminar to turbulent flow.

Formula (Reynolds Number):
$v_c = \frac{R \cdot \eta}{\rho \cdot D}$
Where:

$v_c$ : Critical velocity
$R$ : Reynolds number
$\eta$ : Viscosity
$\rho$ : Density of fluid
$D$ : Diameter of the pipe

8. What is a Thermodynamic System?

Answer:
A thermodynamic system is a defined space or quantity of matter where energy interactions (heat and work) occur.
Types of Systems:

Open System: Both mass and energy can cross the boundary (e.g., engine).
Closed System: Only energy can cross the boundary, not mass (e.g., piston).
Isolated System: Neither mass nor energy crosses the boundary (e.g., thermos flask).

9. State and Prove the Equation of Continuity

Answer:
The equation of continuity ensures mass conservation in fluid flow.

Equation:
$A_1 v_1 = A_2 v_2$
Where:

$A_1, A_2$ : Cross-sectional areas
$v_1, v_2$ : Velocities

Proof:

For incompressible fluids, the mass entering a section equals the mass leaving.
Mass flow rate ( $\rho A v$ ) is constant.
Thus, $A_1 v_1 = A_2 v_2$ .

10. Define Carnot Cycle and Efficiency

Answer:
The Carnot cycle is an ideal reversible cycle that provides maximum efficiency for a heat engine. It consists of two isothermal processes and two adiabatic processes.

Efficiency Formula:
$\eta = 1 - \frac{T_c}{T_h}$
Where:

$T_c$ : Temperature of the cold reservoir
$T_h$ : Temperature of the hot reservoir

11. What is Resonance?

Answer:
Resonance occurs when a system oscillates with maximum amplitude at a particular frequency, known as the natural frequency.

12. State Brewster's Law for Polarization

Answer:
Brewster's law states that light is completely polarized when reflected at an angle $\theta_B$ , where:
$\tan \theta_B = \frac{n_2}{n_1}$
Where:

$n_1, n_2$ : Refractive indices of two media

Here are more common questions with their answers:

13. What is Pascal's Law?

Answer:
Pascal's Law states that in a confined fluid at rest, any change in pressure is transmitted equally in all directions.

Formula:
$P = \frac{F}{A}$
Where:

$P$ : Pressure
$F$ : Force
$A$ : Area

Application:

Hydraulic lifts
Brakes in vehicles

14. What is Bernoulli's Principle?

Answer:
Bernoulli's principle states that for an incompressible and non-viscous fluid, the total mechanical energy remains constant along a streamline.

Equation:
$P + \frac{1}{2} \rho v^2 + \rho gh = \text{constant}$
Where:

$P$ : Pressure
$\rho$ : Density of fluid
$v$ : Velocity of fluid
$g$ : Acceleration due to gravity
$h$ : Height

Application:

Airplane wings
Venturi meters

15. Define Simple Harmonic Motion (SHM)

Answer:
Simple harmonic motion is periodic motion where the restoring force is directly proportional to displacement and acts in the opposite direction.

Equation:
$F = -kx$
Where:

$F$ : Restoring force
$k$ : Spring constant
$x$ : Displacement

Examples:

Pendulum motion
Spring oscillations

16. What is the Zeroth Law of Thermodynamics?

Answer:
The Zeroth Law states that if two systems are in thermal equilibrium with a third system, then they are in thermal equilibrium with each other.

Significance:
It defines the concept of temperature.

17. What is Torque?

Answer:
Torque is the rotational equivalent of force. It measures the tendency of a force to rotate an object around an axis.

Formula:
$\tau = r \cdot F \cdot \sin \theta$
Where:

$\tau$ : Torque
$r$ : Distance from the axis
$F$ : Force applied
$\theta$ : Angle between force and lever arm

18. What is Moment of Inertia?

Answer:
Moment of inertia is the measure of an object's resistance to changes in its rotational motion.

Formula:
$I = \sum m_i r_i^2$
Where:

$I$ : Moment of inertia
$m_i$ : Mass of each particle
$r_i$ : Distance from the axis of rotation

Examples:

Cylinder rolling
Flywheel rotation

19. What is Hooke's Law?

Answer:
Hooke's law states that the force needed to extend or compress a spring is directly proportional to the displacement.

Formula:
$F = -kx$
Where:

$F$ : Force
$k$ : Spring constant
$x$ : Displacement

Limit:
Valid within the elastic limit of the material.

20. What is Capillary Action?

Answer:
Capillary action is the ability of a liquid to flow in narrow spaces without external forces like gravity.

Reason:
It occurs due to cohesion (liquid-liquid attraction) and adhesion (liquid-solid attraction).

Examples:

Water rising in a thin tube
Ink in a pen

21. Define Electric Field

Answer:
The electric field is the region around a charge where its force can be felt by other charges.

Formula:
$E = \frac{F}{q}$
Where:

$E$ : Electric field
$F$ : Force
$q$ : Test charge

22. What is Ohm's Law?

Answer:
Ohm's law states that the current through a conductor is directly proportional to the voltage across it and inversely proportional to the resistance.

Formula:
$V = IR$
Where:

$V$ : Voltage
$I$ : Current
$R$ : Resistance

Applications:

Electric circuits
Electrical devices

23. What is Magnetic Flux?

Answer:
Magnetic flux is the total number of magnetic field lines passing through a surface.

Formula:
$\Phi = B \cdot A \cdot \cos \theta$
Where:

$\Phi$ : Magnetic flux
$B$ : Magnetic field strength
$A$ : Area
$\theta$ : Angle between field and surface

24. What is a Wave?

Answer:
A wave is a disturbance that transfers energy from one point to another without transporting matter.

Types:

Mechanical (e.g., sound, water waves)
Electromagnetic (e.g., light, radio waves)

Wave Equation:
$v = f \lambda$
Where:

$v$ : Velocity
$f$ : Frequency
$\lambda$ : Wavelength

What is Torricelli's Theorem?

Answer:
Torricelli's theorem describes the velocity of a fluid flowing out of an orifice under the influence of gravity. It states that the speed of efflux (the velocity with which the fluid exits) is the same as the velocity an object would acquire if it fell freely from the same height.

Formula:
$v = \sqrt{2gh}$
Where:

$v$ : Velocity of efflux
$g$ : Acceleration due to gravity ( $9.8 \, \text{m/s}^2$ )
$h$ : Height of the fluid above the orifice

Explanation:

The theorem is derived from Bernoulli’s principle and energy conservation.
It assumes the fluid is ideal (non-viscous, incompressible) and the flow is steady.

Applications:

Determining the speed of water exiting a tank.
Designing fountains and water-based systems.

Example:
If the height of water in a tank is $h = 5 \, \text{m}$ , the velocity of efflux is:
$v = \sqrt{2 \times 9.8 \times 5} = 9.9 m/s$

Notice:

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