TS Inter 2nd Year – Physics Previous Paper 2020

PHYSICS, Paper – II

(English Version)

Time: 3 Hours

Max. Marks: 60

Question 1: What are cathode rays?

Answer:

Cathode rays are streams of electrons emitted from the negative electrode (cathode) of a high-voltage vacuum tube. They were discovered by J. J. Thomson in 1897.

Key properties of cathode rays:

Travel in straight lines: They cast sharp shadows when objects are placed in their path.
Carry negative charge: They are deflected by electric and magnetic fields.
Produce heat: When they strike a metal target, they produce heat.
Cause fluorescence: They cause certain materials to glow.
Produce X-rays: When they strike a metal target at high speeds, they produce X-rays.

Question 2: State Heisenberg’s Uncertainty Principle.

Answer:

Heisenberg’s Uncertainty Principle states that it is fundamentally impossible to simultaneously determine both the position and momentum (or velocity) of a particle with absolute certainty.

Mathematically, it is expressed as:

Δx * Δp ≥ h/4π

where:

Δx is the uncertainty in the position of the particle

Δp is the uncertainty in the momentum of the particle
h is Planck’s constant

In simpler terms:

The more precisely you know the position of a particle, the less precisely you can know its momentum (and vice versa). This principle has profound implications for our understanding of the behavior of subatomic particles.

Question 3: Which gates are called Universal Gates?

Answer:

Universal gates are logic gates that can be used to implement any Boolean function or any other logic gate. The most common universal gates are:

NAND Gate: NAND gate is a combination of NOT and AND gates. It produces an output that is the negation of the AND operation.
NOR Gate: NOR gate is a combination of NOT and OR gates. It produces an output that is the negation of the OR operation.

Question 4: Which type of communication is employed in mobile phones?

Answer:

Mobile phones primarily employ electromagnetic wave communication for transmitting and receiving signals. This involves:

Radio waves: For voice calls and text messages.
Microwaves: For cellular networks (2G, 3G, 4G, 5G) to transmit data at higher speeds.

Question 5: What is the magnetic moment associated with a solenoid?

Answer:

The magnetic moment of a solenoid is a measure of its magnetic strength and is given by:

μ = nIA

where:

μ is the magnetic moment
n is the number of turns per unit length of the solenoid
I is the current flowing through the solenoid
A is the cross-sectional area of the solenoid

Question 6: A concave mirror produces an image of a long vertical pin placed 40 cm from the mirror at the position of the object. Find the focal length of the mirror.

Answer:

In this scenario, the image is formed at the same position as the object. This only happens when the object is placed at the center of curvature (C) of the concave mirror.

Since the image is formed at the center of curvature, the object distance (u) is equal to the radius of curvature (R).

Therefore, u = R = 40 cm

We know that the focal length (f) is half the radius of curvature:

f = R/2 = 40 cm / 2 = 20 cm

So, the focal length of the mirror is 20 cm.

Question 7: Define magnetic declination.

Answer:

Magnetic declination is the angle between the direction of the Earth’s magnetic north and the direction of true geographic north at a particular location. It varies from place to place and changes over time.

Question 8: Distinguish between ammeter and voltmeter.

Answer:

Feature	Ammeter	Voltmeter
Function	Measures electric current flowing through a circuit	Measures the potential difference (voltage) across a component in a circuit
Connection	Connected in series with the component	Connected in parallel with the component
Resistance	Ideally has very low resistance	Ideally has very high resistance

Question 9: A power transmission line feeds input power at 2300 V to a step-down transformer with its primary windings having 4000 turns. What should be the number of turns in the secondary in order to get output at 230 V?

Answer:

We can use the transformer equation:

(V₁ / V₂) = (N₁ / N₂)

where:

V₁ is the primary voltage (2300 V)
V₂ is the secondary voltage (230 V)
N₁ is the number of turns in the primary winding (4000 turns)
N₂ is the number of turns in the secondary winding (to be calculated)

Rearranging the equation:

N₂ = (V₂ / V₁) * N₁ = (230 V / 2300 V) * 4000 turns = 400 turns

Therefore, the number of turns in the secondary winding should be 400 turns.

Question 10: What are the applications of microwaves?

Answer:

Microwaves have a wide range of applications, including:

Communication: Cellular phones, satellite communication, radar
Cooking: Microwave ovens
Medical imaging: MRI (Magnetic Resonance Imaging)
Remote sensing: Weather forecasting, satellite imaging

Section: B

Marks: 6 x 4 = 24

Question 11: Explain the formation of a rainbow.

Answer: A rainbow is a meteorological phenomenon caused by the reflection, refraction, and dispersion of light in water droplets. When sunlight enters a raindrop, it is refracted and dispersed into its constituent colors due to the varying refractive index of water with wavelength. This causes different colors to bend at different angles. The light undergoes total internal reflection at the back surface of the raindrop and is refracted again as it exits. The angle between the incoming sunlight and the outgoing rainbow light is about 42 degrees for red light and 40 degrees for violet light. This angular separation forms the rainbow’s arc.

Question 12: How do you determine the resolving power of your eye?

Answer: The resolving power of the eye is its ability to distinguish between two closely spaced objects. It can be determined by measuring the minimum angular separation between two point sources that can be seen as separate. This is usually done using a Snellen chart, where the smallest letters that can be read at a certain distance are used to calculate the resolving power.

Question 13: Derive an expression for the intensity of the electric field at a point on the equatorial plane of an electric dipole.

Answer: Consider an electric dipole with charges +q and -q separated by a distance 2a. The electric field at a point P on the equatorial plane is given by:

$E = \frac{1}{4 \pi \epsilon_0} \frac{q}{r^2} \sin \theta$

$E = \frac{1}{4 π ϵ ^{0}} \frac{q}{r ^{2}} sin θ$

Where:

$\epsilon_0$
$r$
$\theta$

Since the point P is on the equatorial plane, $\theta = 90^\circ$

$θ = 9 0^{\circ}$ , so $\sin \theta = 1$

$sin θ = 1$ . Substituting this, we get:

$E = \frac{1}{4 \pi \epsilon_0} \frac{q}{r^2}$

$E = \frac{1}{4 π ϵ ^{0}} \frac{q}{r ^{2}}$

This is the intensity of the electric field at a point on the equatorial plane of an electric dipole.

Question 14: Derive an expression for the capacitance of a parallel plate capacitor.

Answer: A parallel plate capacitor consists of two parallel conducting plates separated by a distance $d$

$d$ . The capacitance $C$

$C$ of the capacitor is given by:

$C = \frac{\epsilon_0 A}{d}$

$C = \frac{ϵ ^{0} A}{d}$

Where:

$\epsilon_0$
$A$
$d$

This expression is derived using Gauss’s law and the definition of capacitance.

Question 15: State and explain Biot-Savart Law.

Answer: The Biot-Savart Law describes the magnetic field generated by a steady current. It states that the magnetic field at a point due to a current element is directly proportional to the current, the length of the current element, and the sine of the angle between the current element and the line joining the current element to the point. The direction of the magnetic field is given by the right-hand rule.

Mathematically:

$dB = \frac{\mu_0}{4 \pi} \frac{I \, dl \times r}{r^3}$

$d B = \frac{μ ^{0}}{4 π} \frac{I d l \times r}{r ^{3}}$

Where:

$dB$
$\mu_0$
$r$
$\times$

Question 16: Obtain an expression for the magnetic energy stored in a solenoid in terms of magnetic field $B$

$B$ , area $A$

$A$ , and length $L$

$L$ of the solenoid.

Answer: The magnetic energy stored in a solenoid is given by:

$U = \frac{1}{2} \frac{B^2 V}{\mu_0}$

$U = \frac{1}{2} \frac{B ^{2} V}{μ ^{0}}$

Where:

$B$
$V$
$\mu_0$

The volume $V$

$V$ of the solenoid is $A \times L$

$A \times L$ , where $A$

$A$ is the cross-sectional area and $L$

$L$ is the length of the solenoid. Substituting this into the above equation:

$U = \frac{1}{2} \frac{B^2 A L}{\mu_0}$

$U = \frac{1}{2} \frac{B ^{2} A L}{μ ^{0}}$

This is the expression for the magnetic energy stored in a solenoid in terms of $B$

$B$ , $A$

$A$ , and $L$

$L$ .

Question 17: What are the limitations of Bohr’s theory of hydrogen atom?

Answer: Bohr’s theory of the hydrogen atom, although revolutionary, has the following limitations:

It only works for hydrogen-like atoms (atoms with a single electron).
It cannot explain the fine structure of spectral lines.
It does not account for the Zeeman effect (splitting of spectral lines in a magnetic field).
It fails to explain the phenomenon of chemical bonding.

Question 18: Distinguish between half-wave and full-wave rectifiers.

Feature	Half-wave Rectifier	Full-wave Rectifier
Output waveform	Half-wave rectified	Full-wave rectified
Efficiency	Lower	Higher
Ripple factor	Higher	Lower
Number of diodes	1	2 or 4

A half-wave rectifier allows only one half-cycle of the AC input to pass through, while a full-wave rectifier allows both half-cycles to pass through, but with the negative half-cycle inverted. This results in a smoother DC output with a lower ripple factor for the full-wave rectifier.

Section C

Notes:

Answer any two of the following questions.
Each question carries eight marks.
All are Long Answer Type Questions.

Question 19:

Explain the formation of stationary waves in an air column enclosed in an open pipe. Derive the equations for the frequencies of the harmonics produced.

An open organ pipe 30 cm long is sounded. If the velocity of sound is 330 m/s, what is the fundamental frequency of vibration of the air column?

Answer:

Formation of Stationary Waves in an Open Pipe:

In an open pipe, both ends are open to the atmosphere, allowing free movement of air molecules.
When a longitudinal sound wave travels through the pipe, it reflects back and forth from the open ends.
The incident and reflected waves interfere with each other, resulting in the formation of stationary waves.
At the open ends, the air molecules have maximum displacement, creating antinodes.

Modes of Vibration and Frequencies:

Fundamental Mode (First Harmonic):
- The simplest mode of vibration occurs when the length of the pipe (L) is equal to half the wavelength (λ₁) of the sound wave.
- This results in an antinode at both ends and a node at the center of the pipe.
- Mathematically: L = λ₁/2
- Therefore, λ₁ = 2L
- The frequency (f₁) of the fundamental mode is given by:
  - f₁ = v / λ₁ = v / (2L)
- where v is the velocity of sound.
Higher Harmonics:
- In higher harmonics, the pipe contains more than one loop of the stationary wave.
- For the nth harmonic:
  - λₙ = 2L / n
  - fₙ = v / λₙ = n * (v / 2L) = n * f₁
- where n is an integer (n = 1, 2, 3, …).

Fundamental Frequency for the Given Pipe:

Length of the pipe, L = 30 cm = 0.3 m
Velocity of sound, v = 330 m/s
Using the formula for fundamental frequency:
- f₁ = v / (2L) = 330 / (2 * 0.3) = 550 Hz

Therefore, the fundamental frequency of vibration of the air column in the open organ pipe is 550 Hz.

Question 20:

State the working principle of potentiometer. Explain with the help of a circuit diagram, how the potentiometer is used to determine the internal resistance of the given primary cell.

In a potentiometer arrangement, a cell of emf 1.25 V gives a balance point at 35.0 cm length of the wire. If the cell is replaced by another cell and the balance point shifts to 63.0 cm, what is the emf of the second cell?

Answer:

Working Principle of Potentiometer:

A potentiometer is a device used to measure the emf of a cell or the potential difference across a component without drawing any current from it.
It works on the principle of potential gradient. When a constant current flows through a uniform wire, the potential drop per unit length of the wire is constant.

Circuit Diagram and Determination of Internal Resistance:

Circuit:
- A constant current source is connected across a long uniform wire AB.
- The cell whose emf is to be measured (E) is connected in series with a variable resistance (rheostat) and a galvanometer across a portion of the wire.
- A jockey is used to make contact at different points along the wire.
Procedure:
1. With the jockey, find the balancing length (l₁) for the cell E.
2. Connect a known resistance (R) in parallel with the cell.
3. Find the new balancing length (l₂) for the cell with the resistance connected.
4. The internal resistance (r) of the cell can be calculated using the formula:
  - r = R * [(l₁ – l₂) / l₂]

Calculation of EMF of the Second Cell:

Let the emf of the first cell be E₁ = 1.25 V and the balancing length be l₁ = 35.0 cm.
Let the emf of the second cell be E₂ and the balancing length be l₂ = 63.0 cm.
The emf of a cell is directly proportional to the balancing length:
- E₁ / E₂ = l₁ / l₂
- E₂ = (l₂ / l₁) * E₁ = (63.0 cm / 35.0 cm) * 1.25 V = 2.25 V

Therefore, the emf of the second cell is 2.25 V.

Question 21:

Explain the principle and working of a nuclear reactor with the help of a labeled diagram.

Answer:

Principle of Nuclear Reactor:

Nuclear reactors utilize controlled nuclear fission reactions to produce energy.
Fission is a process in which a heavy nucleus (like Uranium-235) splits into two lighter nuclei, releasing a large amount of energy and neutrons.
The released neutrons can then trigger further fission reactions, creating a chain reaction.

Working of a Nuclear Reactor:

Nuclear Fuel:
- The reactor core contains nuclear fuel rods, typically enriched uranium.
- These rods provide the fissile material for the chain reaction.
Moderator:
- A moderator (like water or graphite) is used to slow down the fast-moving neutrons produced in the fission process.
- Slower neutrons are more likely to cause further fission reactions.
Control Rods:
- Control rods (made of materials like boron or cadmium) are inserted into the reactor core to absorb neutrons and control the rate of the chain reaction.
- By adjusting the position of the control rods, the reactor’s power output can be regulated.
Coolant:
- A coolant (like water or liquid sodium) is circulated through the reactor core to remove the heat generated by the fission process.
Shielding:
- A thick concrete or steel shield surrounds the reactor core to protect personnel from harmful radiation.
Heat Exchanger:
- The hot coolant from the reactor core is passed through a heat exchanger, where it transfers heat to a secondary fluid (usually water).
- This secondary fluid is converted into steam, which drives a turbine to generate electricity.

Labeled Diagram of a Nuclear Reactor:

I hope this comprehensive breakdown is helpful! Feel free to ask if you have any more questions or want to explore specific concepts in more detail.