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12th Physics Board Question Paper : Section - B (2 Marks) Important Theory Questions
SECTION - B
Attempt any Eight of the following :
Total Marks - 16
1) Define coefficient of viscosity. State its formula and S.I. units.
Ans : The coefficient of viscosity, also known as dynamic viscosity or simply viscosity, is a measure of a fluid's resistance to deformation or flow. It quantifies how easily a fluid can be sheared or moved. The coefficient of viscosity is denoted by the symbol η (eta).
Formula:
The formula for viscosity (η) is given by:
\[ \text{Viscosity} (\eta) = \frac{\text{Shear Stress}}{\text{Shear Rate}} \]
Where,
- Shear Stress is the force applied parallel to the surface of the fluid per unit area.
- Shear Rate is the rate at which adjacent layers of fluid move with respect to each other.
SI Units:
\(\text{Pa} \cdot \text{s}\) or \(\text{N} \cdot \text{s/m}^2\).
2) Obtain an expression for magnetic induction of a toroid of 'N' turns about an axis passing through its center and perpendicular to its plane.
Ans : To obtain an expression for the magnetic induction (B) inside a toroid with N turns, we can use Ampère's law. For a toroid, Ampère's law is given by:
\[ B \cdot 2\pi r = \mu_0 \cdot N \cdot I \]
Where:
- \( B \) is the magnetic induction inside the toroid.
- \( r \) is the radius of the toroid.
- \( \mu_0 \) is the permeability of free space (\(4\pi \times 10^{-7} \, \text{T} \cdot \text{m/A}\)).
- \( N \) is the number of turns.
- \( I \) is the current flowing through each turn of the toroid.
Now, solve for \( B \) to get the expression:
\[ B = \frac{\mu_0 \cdot N \cdot I}{2\pi r} \]
3) State and prove principle of conservation of angular momentum.
Ans : The principle of conservation of angular momentum states that the total angular momentum of an isolated system remains constant if no external torques act on it. Mathematically, the principle can be expressed as:
\[ \text{Initial Angular Momentum} = \text{Final Angular Momentum} \]
To prove the conservation of angular momentum, let's consider a system where no external torques are acting. The angular momentum (\(L\)) of an object rotating about an axis is given by the product of its moment of inertia (\(I\)) and angular velocity (\(\omega\)):
\[ L = I \omega \]
Now, let's consider an isolated system with no external torques. According to Newton's second law for rotation, the net torque (\(\tau\)) acting on an object is equal to the rate of change of angular momentum (\(\frac{dL}{dt}\)):
\[ \tau = \frac{dL}{dt} \]
In an isolated system (\(\tau_{\text{external}} = 0\)), this equation becomes:
\[ 0 = \frac{dL}{dt} \]
Integrating both sides with respect to time, we get:
\[ \int 0 \, dt = \int \frac{dL}{dt} \, dt \]
This simplifies to:
\[ \text{Constant} = L \]
4) Obtain an expression for equivalent capacitance of two capacitors C1 and C2 connected in series.
Ans : When capacitors are connected in series, the total (equivalent) capacitance, denoted as \( C_{\text{eq}} \), can be found using the reciprocal formula. For two capacitors, C1 and C2, connected in series, the formula is:
\[ \frac{1}{C_{\text{eq}}} = \frac{1}{C_1} + \frac{1}{C_2} \]
This expression holds true for any number of capacitors connected in series; we simply sum the reciprocals of each individual capacitance value.
This formula is derived from the fact that in a series circuit, the charge on each capacitor is the same, but the voltage across each capacitor is different. The reciprocal relationship arises from the fact that the total voltage across capacitors in series is the sum of the individual voltages.
\[ \frac{1}{C_{\text{eq}}} = \frac{1}{C_1} + \frac{1}{C_2} \]
5) Explain, why the equivalent inductance of two coils connected in parallel is less than the inductance of either of the coils.
Ans : Mathematically, for two inductors \(L_1\) and \(L_2\) in parallel, the equivalent inductance (\(L_{\text{eq}}\)) is given by:
\[ \frac{1}{L_{\text{eq}}} = \frac{1}{L_1} + \frac{1}{L_2} \]
This expression clearly shows that the reciprocal of the equivalent inductance is the sum of the reciprocals of the individual inductances. Since the sum is taken in the denominator, the equivalent inductance is always less than the smallest inductance in the parallel combination.
6) How will you convert a moving coil galvanometer into an ammeter?
Ans : 1. Determine the Full-Scale Current (Ig) :
- Identify the full-scale deflection current of the galvanometer (Ig), which is the current that causes the galvanometer to show full-scale deflection.
2. Choose a Shunt Resistor (Rs) :
- Select a low-resistance shunt resistor (Rs) that can handle the full-scale current and is known to provide the desired range for the ammeter. The relationship between the shunt resistance (Rs) and the desired current range (I) is given by Ohm's Law: \(Rs = \frac{G}{I - Ig}\), where G is the galvanometer's resistance.
3. Connect the Shunt Resistor in Parallel :
- Connect the shunt resistor in parallel with the galvanometer.
4. Calculate the Total Current :
- The total current (It) flowing through the parallel combination of the galvanometer and shunt resistor is the sum of the current through the galvanometer (Ig) and the current through the shunt resistor (Is): \(It = Ig + Is\).
5. Verify the Ammeter's Range :
- Ensure that the combination of the galvanometer and shunt resistor acts as an ammeter with the desired current range.
By adding the shunt resistor in parallel, the majority of the current bypasses the galvanometer, and only a fraction proportional to the shunt resistor's value passes through the galvanometer, allowing it to function as an ammeter.
7) Distinguish between free vibrations and forced vibrations (Two points).
Ans :
1. Initiation of Motion:
- Free Vibrations : In free vibrations, the motion of the system is initiated by an initial disturbance or displacement from its equilibrium position, and then the system oscillates without any external force acting on it.
- Forced Vibrations : Forced vibrations occur when an external periodic force is applied to the system.
2. Response to External Forces:
- Free Vibrations : The system undergoing free vibrations oscillates at its natural frequency, which is determined by its inherent properties such as mass, stiffness, and damping.
- Forced Vibrations : In forced vibrations, the system responds to the external periodic force, and the amplitude and frequency of the motion are influenced by the frequency and amplitude of the applied external force.
8) Define moment of inertia of a rotating rigid body. State its SI unit and dimensions.
Ans : The moment of inertia (I) of a rotating rigid body is a measure of its resistance to changes in its state of rotational motion. It depends on the mass distribution of the body and its axis of rotation. The formula for moment of inertia is given by:
\[ I = \int r^2 \, dm \]
For a discrete system of particles, the formula becomes:
\[ I = \sum_{i} m_i \, r_i^2 \]
Where,
- \( m_i \) is the mass of the \(i\)-th particle.
- \( r_i \) is the perpendicular distance from the axis to the \(i\)-th particle.
SI Unit :
The SI unit of moment of inertia is \(\text{kg} \cdot \text{m}^2\).
Dimensions :
The dimensions of moment of inertia are \([\text{M} \cdot \text{L}^2]\).
9) What are polar dielectrics and non polar dielectrics?
Ans : 1. Polar Dielectrics : Polar dielectrics are dielectric materials composed of polar molecules. A polar molecule is one in which the centers of positive and negative charge do not coincide, creating an electric dipole moment. These materials exhibit a net dipole moment even in the absence of an external electric field.
2. Nonpolar Dielectrics : Nonpolar dielectrics are dielectric materials composed of nonpolar molecules. In a nonpolar molecule, the centers of positive and negative charge coincide, resulting in no permanent electric dipole moment. Nonpolar dielectrics do not exhibit a net dipole moment in the absence of an external electric field.
10) What is a thermodynamics process? Give any two types of it.
Ans : A thermodynamic process is a series of changes that occur in a thermodynamic system, resulting in the transformation of the system from an initial state to a final state. During these processes, various thermodynamic properties such as temperature, pressure, volume, and internal energy may change. Thermodynamic processes are essential for understanding and analyzing the behavior of systems in thermodynamics.
Two common types of thermodynamic processes are:
1. Isothermal Process
2. Adiabatic Process
11) Derive an expression for the radius of the nth Bohr orbit of the electron in hydrogen atom.
Ans : The expression for the radius of the nth Bohr orbit (denoted as \(r_n\)) is derived using certain assumptions and quantization conditions. The relevant expression is given by:
\[ r_n = \frac{{\text{constant} \times n^2}}{{Z}} \]
Where:
- \( n \) is the principal quantum number of the orbit.
- \( Z \) is the atomic number of the nucleus (for hydrogen, \(Z = 1\)).
- The constant is derived from fundamental constants and is often expressed in terms of the Bohr radius (\(a_0\)).
The centripetal force (\(F_{\text{centripetal}}\)) required for circular motion is provided by the electrostatic attraction between the electron and the nucleus.
\( F_{\text{centripetal}} = F_{\text{electrostatic}} \)
Bohr postulated that the angular momentum (\(L\)) of the electron is quantized in units of \(\frac{h}{2\pi}\), where \(h\) is the Planck constant.
\( m_ev_nr_n = \frac{nh}{2\pi} \), where \(m_e\) is the electron mass, \(v_n\) is the velocity in the nth orbit, and \(r_n\) is the radius.
Express the centripetal force in terms of the electron's quantities.
\( F_{\text{centripetal}} = \frac{m_ev_n^2}{r_n} \)
Express the electrostatic force using Coulomb's law.
\( F_{\text{electrostatic}} = \frac{1}{4\pi\varepsilon_0}\frac{e^2}{r_n^2} \), where \(e\) is the elementary charge and \(\varepsilon_0\) is the permittivity of free space.
Equate the centripetal force and the electrostatic force, then solve for \(r_n\).
This leads to \( r_n = \frac{{\text{constant} \times n^2}}{{Z}} \).
12) What are harmonics and overtones (Two points)?
Ans : 1. Harmonics : i) Definition :Harmonics are integer multiples of the fundamental frequency in a vibrating system. In the context of waves and sound, harmonics refer to the frequencies that are whole-number multiples of the fundamental frequency. The fundamental frequency is the lowest frequency produced by a vibrating object.
ii) Example : If the fundamental frequency is 100 Hz, the first harmonic would be 100 Hz, the second harmonic (first overtone) would be 200 Hz, the third harmonic (second overtone) would be 300 Hz, and so on.
2. Overtones : i) Definition : Overtones are any higher frequency components present in a complex wave, beyond the fundamental frequency. The term "overtone" is more general than "harmonic" and can include both harmonics (integer multiples of the fundamental) and other frequencies that are not integer multiples.
ii) Example : In a musical instrument or in the human voice, when a note is produced, the sound is often a combination of the fundamental frequency and various overtones. Overtones contribute to the timbre or quality of the sound.
13) Distinguish between potentiometer and voltmeter.
Ans : 1. Potentiometer : i) Potentiometers are often used to measure and compare electromotive forces (emf) or potential differences and are highly accurate for calibration purposes.
ii) The working principle is based on the voltage division across the resistive wire.
2. Voltmeter : i) Voltmeters use a combination of resistors to measure voltage. In analog voltmeters, a pointer moves along a scale to indicate the voltage value, while digital voltmeters convert the voltage into a digital display.
ii) The working principle involves measuring the current flowing through a known resistance or using electronic components to sense and display the voltage.
14) What are mechanical equilibrium and thermal equilibrium?
Ans : 1. Mechanical Equilibrium : Mechanical equilibrium refers to the state of a physical system in which the sum of all external forces acting on it is zero, and the sum of all external torques (or moments) acting on it is also zero.
2. Thermal Equilibrium : Thermal equilibrium refers to the condition in which two or more systems are at the same temperature and, therefore, no net heat transfer occurs between them.
> SECTION - C Three Marks Important Questions
