Important Questions
Practice these important questions to strengthen your understanding
Question 1
Which of the following is NOT a type of dielectric polarization?
Answer:
c
Explanation:
Dielectric polarization occurs due to displacement or alignment of charges within a dielectric material under an external electric field.
Common types include electronic polarization (displacement of electron clouds), orientation polarization (alignment of permanent dipoles), and space charge polarization (accumulation of charges at interfaces).
Magnetic polarization relates to magnetic properties, not dielectric polarization, so it is not a type of dielectric polarization.
Dielectric polarization occurs due to displacement or alignment of charges within a dielectric material under an external electric field.
Common types include electronic polarization (displacement of electron clouds), orientation polarization (alignment of permanent dipoles), and space charge polarization (accumulation of charges at interfaces).
Magnetic polarization relates to magnetic properties, not dielectric polarization, so it is not a type of dielectric polarization.
Question 2
According to Bohr's atomic model, what is the relationship between the kinetic energy \(K\) and the potential energy \(U\) of an electron in a hydrogen atom orbit?
Answer:
The kinetic energy \( K \) is equal to negative one-half of the potential energy \( U \), i.e., \( K = -\frac{1}{2} U \).
Explanation:
From Bohr's model and classical mechanics, total energy \( E = K + U \) and \( K = -\frac{1}{2} U \).
This means kinetic energy is positive and half the magnitude of the negative potential energy.
This relationship is key to understanding energy levels in hydrogen atom.
From Bohr's model and classical mechanics, total energy \( E = K + U \) and \( K = -\frac{1}{2} U \).
This means kinetic energy is positive and half the magnitude of the negative potential energy.
This relationship is key to understanding energy levels in hydrogen atom.
Question 3
Using Ampere’s law, the magnetic field \( B \) at a distance \( r \) from a long straight current-carrying wire is given by:
Answer:
B = \frac{\mu_0 I}{2 \pi r}
Explanation:
Ampere's law applied to a long straight wire gives the magnetic field at distance r as B = (\mu_0 I) / (2 \pi r). This result matches that obtained from the Biot-Savart law and shows the inverse relationship with distance.
Ampere's law applied to a long straight wire gives the magnetic field at distance r as B = (\mu_0 I) / (2 \pi r). This result matches that obtained from the Biot-Savart law and shows the inverse relationship with distance.
Question 4
Which nucleus is expected to be most stable based on binding energy per nucleon?
Answer:
The nucleus with the highest binding energy per nucleon is the most stable.
Among the given options, Iron-56 has the highest binding energy per nucleon, approximately 8.8 MeV.
Therefore, Iron-56 is expected to be the most stable nucleus.
Among the given options, Iron-56 has the highest binding energy per nucleon, approximately 8.8 MeV.
Therefore, Iron-56 is expected to be the most stable nucleus.
Explanation:
Binding energy per nucleon is a measure of how tightly nucleons are bound in the nucleus.
A higher binding energy per nucleon indicates greater stability.
Iron-56 lies near the peak of the binding energy curve, making it the most stable nucleus among common isotopes.
Helium-4 and Carbon-12 have lower binding energies per nucleon, and Uranium-238 is much heavier with lower binding energy per nucleon.
Binding energy per nucleon is a measure of how tightly nucleons are bound in the nucleus.
A higher binding energy per nucleon indicates greater stability.
Iron-56 lies near the peak of the binding energy curve, making it the most stable nucleus among common isotopes.
Helium-4 and Carbon-12 have lower binding energies per nucleon, and Uranium-238 is much heavier with lower binding energy per nucleon.
Question 5
Using dimensional analysis, derive the expression for the speed \( v \) of transverse waves on a stretched string in terms of tension \( T \) and linear mass density \( \mu \).
Answer:
Let the speed \( v \) depend on tension \( T \) (units: N = kg m/s²) and linear mass density \( \mu \) (units: kg/m).
Assume \( v = k T^a \mu^b \), where \( k \) is dimensionless.
Dimensions of \( v \) are m/s.
Dimensions of \( T^a \mu^b \) are \( (kg m/s^2)^a (kg/m)^b = kg^{a+b} m^{a - b} s^{-2a} \).
Equate powers:
For mass: \( a + b = 0 \)
For length: \( a - b = 1 \)
For time: \( -2a = -1 \) so \( a = \frac{1}{2} \).
From mass: \( b = -a = -\frac{1}{2} \).
From length: check \( a - b = \frac{1}{2} - (-\frac{1}{2}) = 1 \), correct.
Therefore,
\( v = k \sqrt{\frac{T}{\mu}} \).
Usually, \( k = 1 \).
Assume \( v = k T^a \mu^b \), where \( k \) is dimensionless.
Dimensions of \( v \) are m/s.
Dimensions of \( T^a \mu^b \) are \( (kg m/s^2)^a (kg/m)^b = kg^{a+b} m^{a - b} s^{-2a} \).
Equate powers:
For mass: \( a + b = 0 \)
For length: \( a - b = 1 \)
For time: \( -2a = -1 \) so \( a = \frac{1}{2} \).
From mass: \( b = -a = -\frac{1}{2} \).
From length: check \( a - b = \frac{1}{2} - (-\frac{1}{2}) = 1 \), correct.
Therefore,
\( v = k \sqrt{\frac{T}{\mu}} \).
Usually, \( k = 1 \).
Explanation:
Dimensional analysis helps find relationships between physical quantities.
By matching units of speed with tension and mass density, we find exponents.
This shows speed depends on square root of tension over linear mass density.
This derivation confirms the known formula for wave speed on a string.
Dimensional analysis helps find relationships between physical quantities.
By matching units of speed with tension and mass density, we find exponents.
This shows speed depends on square root of tension over linear mass density.
This derivation confirms the known formula for wave speed on a string.
Question 6
Choose the correct option based on the Assertion and Reason.
Assertion (A): The direction of electric current is taken as the direction of positive charge flow.
Reason (R): Electrons actually flow in the opposite direction to current.
(a) A is true but R is false.
(b) A is false but R is true.
(c) Both A and R are true and R is the correct explanation of A.
(d) Both A and R are true but R is not the correct explanation of A.
Assertion (A): The direction of electric current is taken as the direction of positive charge flow.
Reason (R): Electrons actually flow in the opposite direction to current.
(a) A is true but R is false.
(b) A is false but R is true.
(c) Both A and R are true and R is the correct explanation of A.
(d) Both A and R are true but R is not the correct explanation of A.
Answer:
Both Assertion and Reason are true and Reason correctly explains Assertion.
By convention, current direction is taken as direction of positive charge flow.
Electrons, which are negatively charged, flow opposite to this direction.
By convention, current direction is taken as direction of positive charge flow.
Electrons, which are negatively charged, flow opposite to this direction.
Explanation:
The conventional current direction is defined as the direction positive charges would move.
Since electrons carry negative charge, their actual flow is opposite to the conventional current direction.
This explains why the Reason correctly explains the Assertion.
The conventional current direction is defined as the direction positive charges would move.
Since electrons carry negative charge, their actual flow is opposite to the conventional current direction.
This explains why the Reason correctly explains the Assertion.
Question 7
77. True or False: The induced emf in a coil is zero if the magnetic flux through the coil remains constant.
Answer:
True
Explanation:
Faraday’s law states emf is induced only when magnetic flux changes.
If flux is constant, rate of change is zero.
Hence, no emf is induced.
This is a fundamental concept in electromagnetic induction.
Faraday’s law states emf is induced only when magnetic flux changes.
If flux is constant, rate of change is zero.
Hence, no emf is induced.
This is a fundamental concept in electromagnetic induction.
Question 8
Which of the following correctly expresses the wave velocity v in terms of angular frequency \( \omega \) and wave number \( k \)?
Answer:
The wave velocity v is given by the ratio of angular frequency to wave number.
Mathematically, v = \( \frac{\omega}{k} \).
Mathematically, v = \( \frac{\omega}{k} \).
Explanation:
The wave velocity is defined as the speed at which a point of constant phase travels along the medium.
From the wave function, the phase is \( kx - \omega t \).
Keeping the phase constant and differentiating with respect to time gives the velocity as \( v = \frac{\omega}{k} \).
This is a fundamental relation for all progressive waves.
The wave velocity is defined as the speed at which a point of constant phase travels along the medium.
From the wave function, the phase is \( kx - \omega t \).
Keeping the phase constant and differentiating with respect to time gives the velocity as \( v = \frac{\omega}{k} \).
This is a fundamental relation for all progressive waves.
Question 9
Match the terms in column 1 with their correct descriptions in column 2 Magnetic flux \( \Phi_B \) Magnetic field \( B \) Area vector \( \vec{A} \) Angle \( \theta \) Weber (Wb)
Answer:
3,4,2,5,1
Explanation:
Magnetic flux \( \Phi_B \) is the magnetic flux through the surface (3). Magnetic field \( B \) is the magnetic field strength (4). Area vector \( \vec{A} \) is the vector perpendicular to the surface area (2). Angle \( \theta \) is the angle between \( \vec{B} \) and \( \vec{A} \) (5). Weber (Wb) is the SI unit of magnetic flux (1).
Magnetic flux \( \Phi_B \) is the magnetic flux through the surface (3). Magnetic field \( B \) is the magnetic field strength (4). Area vector \( \vec{A} \) is the vector perpendicular to the surface area (2). Angle \( \theta \) is the angle between \( \vec{B} \) and \( \vec{A} \) (5). Weber (Wb) is the SI unit of magnetic flux (1).
Question 10
Why is the path of light inside a prism symmetric at the angle of minimum deviation?
Answer:
The path is symmetric because angles of incidence and emergence are equal, making internal angles equal.
Explanation:
Symmetry at minimum deviation means the light ray bends equally entering and leaving the prism.
This symmetry simplifies calculations and is used to find refractive index.
Other options are incorrect as prism angle is not zero and light does not travel straight inside.
Symmetry at minimum deviation means the light ray bends equally entering and leaving the prism.
This symmetry simplifies calculations and is used to find refractive index.
Other options are incorrect as prism angle is not zero and light does not travel straight inside.
Question 11
Why is a longer uniform wire preferred in a meter bridge experiment?
Answer:
The correct answer is option 3. It improves the accuracy of balance length measurement.
Explanation:
In a meter bridge experiment, the balance length is measured along the wire to determine the unknown resistance.
A longer uniform wire provides a larger scale over which the balance point can be accurately located.
This reduces the relative error in length measurement, improving the accuracy of the resistance determination.
Options such as increasing current or reducing resistance of the wire are not the primary reasons for preferring a longer wire.
Decreasing power consumption is also not directly related to the wire length in this context.
In a meter bridge experiment, the balance length is measured along the wire to determine the unknown resistance.
A longer uniform wire provides a larger scale over which the balance point can be accurately located.
This reduces the relative error in length measurement, improving the accuracy of the resistance determination.
Options such as increasing current or reducing resistance of the wire are not the primary reasons for preferring a longer wire.
Decreasing power consumption is also not directly related to the wire length in this context.
Question 12
Which of the following describes a step-down transformer?
Answer:
A step-down transformer is described by option B: a transformer where the number of turns in the secondary coil \(N_s\) is less than that in the primary coil \(N_p\), and the secondary voltage \(V_s\) is less than the primary voltage \(V_p\).
Explanation:
In a step-down transformer, the secondary coil has fewer turns than the primary coil, resulting in a lower secondary voltage. This matches option B. The other options describe step-up or equal voltage transformers.
In a step-down transformer, the secondary coil has fewer turns than the primary coil, resulting in a lower secondary voltage. This matches option B. The other options describe step-up or equal voltage transformers.
Question 13
The ______ of electric field lines in a region is proportional to the strength of the electric field there.
Answer:
density
Explanation:
The density of electric field lines indicates how strong the electric field is at a point.
Where lines are closer together, the field is stronger.
Where lines are farther apart, the field is weaker.
The density of electric field lines indicates how strong the electric field is at a point.
Where lines are closer together, the field is stronger.
Where lines are farther apart, the field is weaker.
Question 14
True or False Magnetic flux has a direction associated with it
Answer:
False
Explanation:
Magnetic flux is defined as the dot product of the magnetic field vector and the area vector. Since the dot product results in a scalar quantity, magnetic flux does not have a direction associated with it. It only has magnitude. Therefore, the statement that magnetic flux has a direction is false.
Magnetic flux is defined as the dot product of the magnetic field vector and the area vector. Since the dot product results in a scalar quantity, magnetic flux does not have a direction associated with it. It only has magnitude. Therefore, the statement that magnetic flux has a direction is false.
Question 15
Huygens' Principle is fundamental in explaining which types of optical phenomena?
Answer:
option3
Explanation:
Huygens' Principle explains how wavefronts propagate and can be used to derive laws of reflection and refraction, which are part of geometric optics. It also explains wave phenomena like diffraction, which belong to wave optics. Therefore, it is fundamental to both geometric and wave optics phenomena.
Huygens' Principle explains how wavefronts propagate and can be used to derive laws of reflection and refraction, which are part of geometric optics. It also explains wave phenomena like diffraction, which belong to wave optics. Therefore, it is fundamental to both geometric and wave optics phenomena.
Question 16
Explain how an induced emf is generated in a coil when the magnetic flux changes.
Answer:
An induced emf is generated when there is a change in magnetic flux through the coil.
This change can occur by varying the magnetic field strength, the area of the coil, or the angle between the field and the coil.
The changing flux induces an emf according to Faraday's law, which drives a current if the circuit is closed.
This change can occur by varying the magnetic field strength, the area of the coil, or the angle between the field and the coil.
The changing flux induces an emf according to Faraday's law, which drives a current if the circuit is closed.
Explanation:
Magnetic flux through a coil is the product of magnetic field, area, and the cosine of the angle between them.
Any change in these parameters changes the flux.
Faraday's law states that this change induces an emf.
The induced emf causes current flow if the coil circuit is closed.
This phenomenon is the basis for electrical generators and transformers.
Magnetic flux through a coil is the product of magnetic field, area, and the cosine of the angle between them.
Any change in these parameters changes the flux.
Faraday's law states that this change induces an emf.
The induced emf causes current flow if the coil circuit is closed.
This phenomenon is the basis for electrical generators and transformers.
Question 17
Derive the formula for the beat frequency produced by the superposition of two sound waves with frequencies \( f_1 \) and \( f_2 \).
Answer:
Consider two waves:
y_1 = a \sin (2 \pi f_1 t), y_2 = a \sin (2 \pi f_2 t)
Their superposition is:
y = y_1 + y_2 = 2a \cos \left( \pi (f_1 - f_2) t \right) \sin \left( 2 \pi \frac{f_1 + f_2}{2} t \right)
The amplitude varies with time as \(2a \cos (\pi (f_1 - f_2) t)\).
The beat frequency is the frequency of amplitude modulation:
\[ f_{beat} = |f_1 - f_2| \]
y_1 = a \sin (2 \pi f_1 t), y_2 = a \sin (2 \pi f_2 t)
Their superposition is:
y = y_1 + y_2 = 2a \cos \left( \pi (f_1 - f_2) t \right) \sin \left( 2 \pi \frac{f_1 + f_2}{2} t \right)
The amplitude varies with time as \(2a \cos (\pi (f_1 - f_2) t)\).
The beat frequency is the frequency of amplitude modulation:
\[ f_{beat} = |f_1 - f_2| \]
Explanation:
Superposition of two waves with close frequencies results in a wave whose amplitude varies periodically.
This amplitude variation frequency is the beat frequency.
The derivation uses trigonometric identities for sum of sine functions.
The beat frequency equals the absolute difference of the two frequencies.
Superposition of two waves with close frequencies results in a wave whose amplitude varies periodically.
This amplitude variation frequency is the beat frequency.
The derivation uses trigonometric identities for sum of sine functions.
The beat frequency equals the absolute difference of the two frequencies.
Question 18
The work function of a metal is \( 2.0 \) eV. Calculate the threshold frequency and the stopping potential when the metal is illuminated with light of wavelength \( 400 \) nm. (Use \( h = 6.63 \times 10^{-34} \) Js, \( c = 3 \times 10^{8} \) m/s, \( 1 \text{ eV} = 1.6 \times 10^{-19} \) J)
Answer:
Step 1 Convert work function to joules: phi naught equals 2.0 times 1.6 times 10 to the minus 19 equals 3.2 times 10 to the minus 19 joules.
Step 2 Calculate threshold frequency nu naught equals phi naught divided by h equals (3.2 times 10 to the minus 19) divided by (6.63 times 10 to the minus 34) equals 4.83 times 10 to the 14 hertz.
Step 3 Calculate energy of incident photons E equals h c over lambda equals (6.63 times 10 to the minus 34) times (3 times 10 to the 8) divided by (400 times 10 to the minus 9) equals 4.97 times 10 to the minus 19 joules.
Step 4 Calculate stopping potential V naught equals (E minus phi naught) divided by e equals (4.97 times 10 to the minus 19 minus 3.2 times 10 to the minus 19) divided by (1.6 times 10 to the minus 19) equals 1.06 volts.
Step 2 Calculate threshold frequency nu naught equals phi naught divided by h equals (3.2 times 10 to the minus 19) divided by (6.63 times 10 to the minus 34) equals 4.83 times 10 to the 14 hertz.
Step 3 Calculate energy of incident photons E equals h c over lambda equals (6.63 times 10 to the minus 34) times (3 times 10 to the 8) divided by (400 times 10 to the minus 9) equals 4.97 times 10 to the minus 19 joules.
Step 4 Calculate stopping potential V naught equals (E minus phi naught) divided by e equals (4.97 times 10 to the minus 19 minus 3.2 times 10 to the minus 19) divided by (1.6 times 10 to the minus 19) equals 1.06 volts.
Explanation:
Convert the work function from electronvolts to joules for calculation.
Threshold frequency is work function divided by Planck's constant.
Calculate photon energy from the given wavelength.
Stopping potential is the difference between photon energy and work function divided by electron charge.
This shows how stopping potential depends on incident light wavelength and material properties.
Convert the work function from electronvolts to joules for calculation.
Threshold frequency is work function divided by Planck's constant.
Calculate photon energy from the given wavelength.
Stopping potential is the difference between photon energy and work function divided by electron charge.
This shows how stopping potential depends on incident light wavelength and material properties.
Question 19
Fill in the blank: Standard analog video signals typically require bandwidths up to _____ MHz.
Answer:
6
Explanation:
Standard analog video signals require bandwidths up to about 6 MHz.
This bandwidth accommodates both picture and audio information.
It is much higher than audio bandwidth requirements.
Standard analog video signals require bandwidths up to about 6 MHz.
This bandwidth accommodates both picture and audio information.
It is much higher than audio bandwidth requirements.
Question 20
In magnetic braking, eddy currents produce a force that:
Answer:
b
Explanation:
Eddy currents induced in a conductor moving in a magnetic field produce a force that opposes the motion, thereby slowing the object down (magnetic braking).
They do not accelerate the object, only generate heat, or increase magnetic field strength.
Eddy currents induced in a conductor moving in a magnetic field produce a force that opposes the motion, thereby slowing the object down (magnetic braking).
They do not accelerate the object, only generate heat, or increase magnetic field strength.
