TS Inter 2nd Year – Physics Previous Paper 2023
PHYSICS, Paper – II
(English Version)
Time: 3 Hours] [Max. Marks: 60
SECTION-A
Note: (i) Answer ALL Questions. (ii) Each Question carries TWO marks. (iii) All are very short answer type questions.
1. What is the principle of a moving coil galvanometer?
Answer:
The principle of a moving coil galvanometer is based on the torque experienced by a current-carrying coil placed in a uniform magnetic field. When a current flows through the coil, it experiences a torque due to the interaction between the magnetic field and the current. This torque causes the coil to rotate, and the deflection of the coil is proportional to the current flowing through
2. Define magnetic inclination or angle of dip.
Answer:
Magnetic inclination or angle of dip is the angle that the Earth’s magnetic field lines make with the horizontal at a particular location. It is the angle between the direction of the Earth’s magnetic field and the horizontal plane. At the magnetic equator, the angle of dip is zero, while at the magnetic poles, it is 90 degrees.
3. A small angled prism of 4° deviates a ray through 2.48°. Find the refractive index of the prism.
Answer:
For a small-angled prism, the angle of deviation (δ) is related to the angle of the prism (A) and the refractive index (μ) by the following formula:
δ = (μ – 1)A
where,
- δ = angle of deviation = 2.48°
- A = angle of the prism = 4°
Rearranging the formula to find the refractive index:
μ = (δ/A) + 1
Substituting the values:
μ = (2.48°/4°) + 1
μ = 0.62 + 1
μ = 1.62
Therefore, the refractive index of the prism is 1.62.
4. Classify the following materials with regard to magnetism: Manganese, Cobalt, Nickel, Bismuth, Oxygen, Copper.
Answer:
- Ferromagnetic: Cobalt, Nickel
- Paramagnetic: Manganese, Oxygen
- Diamagnetic: Bismuth, Copper
5. What important fact did Millikan’s experiment establish?
Answer: Millikan’s oil drop experiment established that electric charge is quantized. It showed that the charge on any object is an integral multiple of a fundamental unit of charge, which is the charge of an electron.
6. A transformer converts 200 V ac into 2000 V ac. Calculate the number of turns in the secondary if the primary has 10 turns.
Answer:
In a transformer, the ratio of the number of turns in the secondary coil (Ns) to the number of turns in the primary coil (Np) is equal to the ratio of the
Ns/Np = Vs/Vp
Given:
- Vp = 200 V
- Vs = 2000 V
- Np = 10 turns
Substituting the values:
Ns/10 = 2000/200
Ns = 10 * 10
Ns = 100 turns
Therefore, the number of turns in the secondary coil is 100.
7. If the wavelength of electromagnetic radiation is doubled, what happens to the energy of photon?
Answer:
The energy of a photon is inversely proportional to its wavelength.
E = hc/λ
where:
- E is the energy of the photon
- h is Planck’s constant
- c is the speed of light
- λ is the wavelength of the radiation
If the wavelength (λ) is doubled, the energy (E) of the photon will be halved.
8. Give examples of “photosensitive substances”. Why are they called so?
Answer:
Examples of photosensitive substances include:
- Selenium
- Silver Halides (like silver bromide and silver chloride)
- Cadmium Sulfide
- Silicon
These substances are called photosensitive because they exhibit a change in their electrical properties, such as conductivity or voltage, when exposed to light. This change is due to the photoelectric effect, where photons of light interact with the electrons in the material, causing them to be ejected.
9. What is sky wave propagation?
Answer:
Skywave propagation is a type of radio wave propagation where radio waves are transmitted from the Earth’s surface, reflected by the ionosphere, and then received back on Earth at a distant location. The ionosphere is a layer of the Earth’s atmosphere that contains charged particles, which can reflect radio waves. This type of propagation allows for long-distance communication over great distances.
10. Write the truth table of NAND gate. How does it differ from AND gate?
Answer:
Truth Table for NAND Gate:
| Input A | Input B | Output (Y) |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
Difference between NAND and AND Gate:
- Output: The output of a NAND gate is the negation of the output of an AND gate. In other words, if both inputs to an AND gate are 1, the output is 1; in a NAND gate, the output is 0 in this case.
SECTION – B
Note: (i) Answer ANY SIX questions. (ii) Each question carries FOUR marks. (iii) All are of short answer type questions.
11. Distinguish between half-wave and full-wave rectifiers.
Half-wave rectifier:
- Converts only one half-cycle of the AC input into DC output.
- Uses a single diode.
- Output has a large ripple factor.
- Lower efficiency compared to full-wave rectifiers.
Full-wave rectifier:
- Converts both half-cycles of the AC input into DC output.
- Uses two diodes in a bridge configuration or a center-tapped transformer.
- Output has a smaller ripple factor compared to half-wave rectifiers.
- Higher efficiency compared to half-wave rectifiers.
12. Describe the ways in which Eddy currents are used to advantage.
Eddy currents are induced currents that circulate within a conductor when it is subjected to a changing magnetic field. These currents can be used to advantage in various applications:
- Magnetic braking: Eddy currents are used in braking systems of trains and roller coasters. When a brake shoe is applied to a moving wheel, eddy currents are induced in the wheel, which oppose the motion and bring the wheel to a stop.
- Induction heating: Eddy currents are used to heat metals in induction furnaces. The rapidly changing magnetic field induces eddy currents in the metal, which generate heat due to resistive losses.
- Eddy current testing: Eddy currents are used to detect flaws and defects in metals. Changes in the conductivity of the metal due to flaws affect the eddy current flow, which can be detected by sensors.
- Speedometers: Eddy currents are used in some types of speedometers. A rotating disc interacts with a magnetic field, inducing eddy currents that generate a torque proportional to the speed of the vehicle.
13. Write a short note on De Broglie’s explanation of Bohr’s second postulate of quantization.
De Broglie’s explanation of Bohr’s second postulate of quantization:
Bohr’s second postulate states that the angular momentum of an electron revolving around the nucleus in a stable orbit is quantized, i.e., it can only take certain discrete values. De Broglie explained this postulate by proposing that electrons have wave-like properties. He suggested that the electron’s orbit must be a standing wave, meaning that the circumference of the orbit must be an integral multiple of the electron’s wavelength. This condition ensures that the electron’s wave does not interfere with itself destructively, maintaining a stable orbit.
14. Derive an expression for the magnetic dipole moment of a revolving electron.
Derivation of magnetic dipole moment of a revolving electron:
The magnetic dipole moment (μ) of a current loop is given by:
μ = IA
where,
- I is the current flowing through the loop
- A is the area of the loop
For an electron revolving in a circular orbit of radius r with a speed v, the current (I) can be expressed as:
I = (charge of electron) / (time period of revolution)
I = e / (2πr/v) = ev/2πr
where,
- e is the charge of the electron
The area of the orbit is A = πr^2
Therefore, the magnetic dipole moment of the revolving electron is:
μ = (ev/2πr) * πr^2 = (evr)/2
15. Define critical angle. Explain total internal reflection using a neat diagram.
Critical Angle:
The critical angle is the angle of incidence in a denser medium at which the angle of refraction in the rarer medium becomes 90 degrees.
Total Internal Reflection:
Total internal reflection occurs when a light ray traveling from a denser medium to a rarer medium strikes the interface
Diagram:
16. Explain Doppler effect in light. Distinguish between red shift and blue shift.
Doppler Effect in Light:
The Doppler effect is the change in frequency or wavelength of a wave (such as light or sound) due to the relative motion between the source
Red Shift:
- Occurs when the source of light is moving away from the observer.
- The wavelength of the light increases and the frequency decreases.
- Observed in the spectra of distant galaxies, indicating that the universe is expanding.
Blue Shift:
- Occurs when the source of light is moving towards the observer.
- The wavelength of the light decreases and the frequency increases.
- Observed in the spectra of certain stars and galaxies.
17. Derive an expression for the capacitance of a parallel plate capacitor.
Derivation of Capacitance of Parallel Plate Capacitor:
Consider a parallel plate capacitor with plate area A and separation d. Let the charge on each plate be +Q and -Q. The electric field between the plates is given by:
E = σ/ε₀ = Q/(ε₀A)
where,
- σ is the surface charge density
- ε₀ is the permittivity of free space
The potential difference (V) between the plates is:
V = Ed = (Q/ε₀A) * d
The capacitance (C) is defined as the ratio of charge (Q) to the potential difference (V):
C = Q/V = Q / [(Q/ε₀A) * d]
Therefore, the capacitance of a parallel plate capacitor is:
C = ε₀A/d
18. State Gauss’s law in electrostatics.
Gauss’s Law in Electrostatics:
Gauss’s law states that the total electric flux through any closed surface is equal to the net charge enclosed by the surface divided by the permittivity of free space
∮E⋅dA = Q/ε₀
where,
- E is the electric field vector
- dA is an infinitesimal area element of the closed surface
- Q is the net charge enclosed by the surface
- ε₀ is the permittivity of free space
SECTION – C
Note: (i) Answer ANY TWO questions. (ii) Each question carries EIGHT marks. (iii) All are long answer type questions.
19. How are stationary waves formed in closed pipes? Explain the various modes of vibrations and obtain relations for their frequencies.
A closed organ pipe 70 cm long is sounded. If the velocity of sound is 331 m/s, what is the fundamental frequency of vibration of the air column?
Formation of Stationary Waves in Closed Pipes:
- In a closed pipe, one end is closed and the other is open.
- When a sound wave is produced at the open end, it travels down the pipe and gets reflected at the closed end.
- The incident and reflected waves interfere, resulting in the formation of stationary waves with nodes and antinodes.
Modes of Vibration and Frequencies:
-
Fundamental Mode (First Harmonic):
- The fundamental mode occurs when there is a node at the closed end and an antinode at the open end.
- The wavelength of the fundamental mode is four times the length of the pipe (λ = 4L).
- The fundamental frequency (f₁) is given by: f₁ = v/λ = v/4L
-
First Overtone (Third Harmonic):
- In the first overtone, there are two nodes and two antinodes.
- The wavelength of the first overtone is four-thirds the length of the pipe (λ = 4L/3).
- The frequency of the first overtone (f₃) is: f₃ = 3v/4L = 3f₁
-
Higher Harmonics:
- Only odd harmonics are possible in a closed pipe.
- The general formula for the frequency of the nth harmonic in a closed pipe is: fₙ = (2n – 1)v/4L, where n = 1, 3, 5, …
Calculation of Fundamental Frequency:
Given:
- Length of the pipe (L) = 70 cm = 0.7 m
- Velocity of sound (v) = 331 m/s
Using the formula for the fundamental frequency:
f₁ = v/4L = 331 / (4 * 0.7) = 331 / 2.8 ≈ 118.2 Hz
Therefore, the fundamental frequency of vibration of the air column is approximately 118.2 Hz.
20. What is radioactivity? State the law of radioactive decay. Show that radioactive decay is exponential in nature.
The half life
Radioactivity:
Radioactivity is the spontaneous emission of particles or electromagnetic radiation from the nucleus of an unstable atom.
Law of Radioactive Decay:
The law of radioactive decay states that the rate of decay of a radioactive substance is directly proportional to the number of radioactive nuclei present at that time. Mathematically, it can be expressed as:
dN/dt = -λN
where,
- N is the number of radioactive nuclei present at time t
- dN/dt is the rate of decay
- λ is the decay constant, which is a characteristic property of the radioactive substance
Exponential Nature of Radioactive Decay:
The solution to the above differential equation gives the exponential decay law:
N(t) = N₀e^(-λt)
where,
- N(t) is the number of radioactive nuclei remaining at time t
- N₀ is the initial number of radioactive nuclei
- e is the base of natural logarithm
- λ is the decay constant
- t is the time
This equation shows that the number of radioactive nuclei decreases exponentially with time.
Calculation of Time for Radium Decay:
Given:
- Half-life of radium (T₁/₂ = 1600 years)
- Initial mass of radium (N₀) = 1 g
- Final mass of radium (N(t)) = 0.125 g
We know that:
T₁/₂ = ln(2)/λ
Therefore,
λ = ln(2)/T₁/₂ = ln(2)/1600
Now, using the decay equation:
N(t) = N₀e^(-λt)
0.125 = 1 * e^(-ln(2)/1600 * t)
Taking natural logarithm on both sides:
ln(0.125) = -ln(2)/1600 * t
t = -ln(0.125) * 1600 / ln(2)
t = 3 * 1600 = 4800 years
Therefore, it takes 4800 years for 1g of radium to reduce to 0.125g.
21. State Kirchhoff’s laws for an electrical network. Using these laws deduce the condition for balance in a Wheatstone Bridge.
Kirchhoff’s Laws:
- Kirchhoff’s Current Law (KCL): The sum of currents flowing into a junction in an electrical circuit is equal to the sum of currents flowing out of that junction.
- Kirchhoff’s Voltage Law (KVL): The sum of the voltage drops across all the elements in a closed loop in an electrical circuit is equal to the sum of the electromotive forces (EMFs) in that loop.
Condition for Balance in a Wheatstone Bridge:
A Wheatstone bridge is an electrical circuit used to measure an unknown resistance. It consists of four resistors connected in a diamond shape.
Let R₁, R₂, R₃, and R₄ be the resistances of the four arms of the bridge. When the bridge is balanced, no current flows through the galvanometer connected between the midpoints of the opposite arms.
Applying Kirchhoff’s laws to the Wheatstone bridge circuit, it can be shown that the condition for balance is:
R₁/R₂ = R₃/R₄
This means that when the bridge is balanced, the ratio of the resistances in the adjacent arms is equal.