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Questions and Answers
A particle executes SHM with an amplitude of $A$. At what displacement from the mean position is its kinetic energy equal to its potential energy?
A particle executes SHM with an amplitude of $A$. At what displacement from the mean position is its kinetic energy equal to its potential energy?
- $A/3$
- $A/\sqrt{2}$ (correct)
- $A/\sqrt{3}$
- $A/2$
The total energy of a particle executing SHM is proportional to which of the following?
The total energy of a particle executing SHM is proportional to which of the following?
- Length of the pendulum
- Square of the amplitude of oscillation (correct)
- Amplitude of oscillation
- Velocity of the particle
A simple pendulum has a time period $T_1$ when on the Earth's surface and $T_2$ when taken to a height $R$ above the Earth's surface, where $R$ is the radius of the Earth. What is the ratio $T_2/T_1$?
A simple pendulum has a time period $T_1$ when on the Earth's surface and $T_2$ when taken to a height $R$ above the Earth's surface, where $R$ is the radius of the Earth. What is the ratio $T_2/T_1$?
- 4
- 1
- 2 (correct)
- $\sqrt{2}$
Two simple harmonic motions are represented by the equations $y_1 = 10\sin(\omega t)$ and $y_2 = 10\sin(\omega t + \pi/2)$. What is the amplitude of the resultant motion?
Two simple harmonic motions are represented by the equations $y_1 = 10\sin(\omega t)$ and $y_2 = 10\sin(\omega t + \pi/2)$. What is the amplitude of the resultant motion?
A charged particle is oscillating in SHM. Which of the following quantities will radiate electromagnetic waves?
A charged particle is oscillating in SHM. Which of the following quantities will radiate electromagnetic waves?
What happens to the frequency of a simple pendulum if its length is doubled?
What happens to the frequency of a simple pendulum if its length is doubled?
A spring-mass system oscillates with a frequency $f$. If the spring is cut into two equal parts and the same mass oscillates with one part, what is the new frequency?
A spring-mass system oscillates with a frequency $f$. If the spring is cut into two equal parts and the same mass oscillates with one part, what is the new frequency?
The equation of SHM is given by $x = 5\sin(2\pi t + \pi/4)$, where x is in meters and t is in seconds. What is the initial displacement at $t=0$?
The equation of SHM is given by $x = 5\sin(2\pi t + \pi/4)$, where x is in meters and t is in seconds. What is the initial displacement at $t=0$?
When a body executes SHM, what is the phase difference between its velocity and acceleration?
When a body executes SHM, what is the phase difference between its velocity and acceleration?
A particle is subjected to two SHMs given by $x = A\sin(\omega t)$ and $y = A\sin(\omega t + \pi/2)$. What is the nature of the resultant motion?
A particle is subjected to two SHMs given by $x = A\sin(\omega t)$ and $y = A\sin(\omega t + \pi/2)$. What is the nature of the resultant motion?
Two charges of equal magnitude and opposite sign are separated by a certain distance. The electrostatic potential at a point midway between the charges is:
Two charges of equal magnitude and opposite sign are separated by a certain distance. The electrostatic potential at a point midway between the charges is:
If the distance between two point charges is doubled, by what factor does the electrostatic force between them change?
If the distance between two point charges is doubled, by what factor does the electrostatic force between them change?
A capacitor is charged and then isolated. If the distance between its plates is increased, how does the electric potential difference between the plates change?
A capacitor is charged and then isolated. If the distance between its plates is increased, how does the electric potential difference between the plates change?
Three identical charges are placed at the vertices of an equilateral triangle. What is the net electrostatic force on any one charge due to the other two?
Three identical charges are placed at the vertices of an equilateral triangle. What is the net electrostatic force on any one charge due to the other two?
Two point charges $+q$ and $-q$ are placed a distance $d$ apart. What is the magnitude of the electric field at a point midway between the charges?
Two point charges $+q$ and $-q$ are placed a distance $d$ apart. What is the magnitude of the electric field at a point midway between the charges?
A parallel-plate capacitor has a capacitance $C_0$ in air. If a dielectric of dielectric constant $K$ is inserted between the plates, what is the new capacitance?
A parallel-plate capacitor has a capacitance $C_0$ in air. If a dielectric of dielectric constant $K$ is inserted between the plates, what is the new capacitance?
What is the effect of increasing the frequency of the driving force on the amplitude of a damped harmonic oscillator near resonance?
What is the effect of increasing the frequency of the driving force on the amplitude of a damped harmonic oscillator near resonance?
In an LCR series circuit, what is the condition for resonance?
In an LCR series circuit, what is the condition for resonance?
A point charge $q$ is placed inside a cube. What is the electric flux through one face of the cube?
A point charge $q$ is placed inside a cube. What is the electric flux through one face of the cube?
The time period of a simple pendulum is measured to be $T$. If the length of the pendulum is increased by 4%, what will be the approximate percentage change in the time period?
The time period of a simple pendulum is measured to be $T$. If the length of the pendulum is increased by 4%, what will be the approximate percentage change in the time period?
The electrostatic force between two charges is 10 N. If the distance between them is halved, what does the force become?
The electrostatic force between two charges is 10 N. If the distance between them is halved, what does the force become?
A capacitor of capacitance C is charged to a potential V and then disconnected from the battery. If a dielectric slab of dielectric constant K is inserted between the plates, how does the stored energy change?
A capacitor of capacitance C is charged to a potential V and then disconnected from the battery. If a dielectric slab of dielectric constant K is inserted between the plates, how does the stored energy change?
Two SHMs with the same frequency have amplitudes $A$ and $2A$. If they are superimposed with a phase difference of $\pi/2$, what is the amplitude of the resultant SHM?
Two SHMs with the same frequency have amplitudes $A$ and $2A$. If they are superimposed with a phase difference of $\pi/2$, what is the amplitude of the resultant SHM?
A charged particle moves in a circle under the influence of a constant magnetic field. If the frequency of revolution is $f$, what happens to the frequency if the kinetic energy of the particle is doubled?
A charged particle moves in a circle under the influence of a constant magnetic field. If the frequency of revolution is $f$, what happens to the frequency if the kinetic energy of the particle is doubled?
What is the effect on the time period of a simple pendulum if the effective 'g' is decreased?
What is the effect on the time period of a simple pendulum if the effective 'g' is decreased?
A cube of side 'a' has a charge 'q' at its center. What is the electric flux through one of the faces of the cube?
A cube of side 'a' has a charge 'q' at its center. What is the electric flux through one of the faces of the cube?
Two identical conducting spheres have charges q and -3q respectively. If they are brought into contact and then separated by the same distance, what is the new electrostatic force between them?
Two identical conducting spheres have charges q and -3q respectively. If they are brought into contact and then separated by the same distance, what is the new electrostatic force between them?
A parallel plate capacitor has a potential difference V between its plates. If both the plate separation and the area of the plates are doubled, how does the potential difference change assuming the charge remains constant?
A parallel plate capacitor has a potential difference V between its plates. If both the plate separation and the area of the plates are doubled, how does the potential difference change assuming the charge remains constant?
A body executes SHM. When its displacement from the mean position is 2 cm, its velocity is 2 cm/s, and when the displacement is 3 cm, its velocity is 1 cm/s. What is the angular frequency of the SHM?
A body executes SHM. When its displacement from the mean position is 2 cm, its velocity is 2 cm/s, and when the displacement is 3 cm, its velocity is 1 cm/s. What is the angular frequency of the SHM?
What is the effect on the electric field at a point if the charge creating the field is doubled and the distance to the point is also doubled?
What is the effect on the electric field at a point if the charge creating the field is doubled and the distance to the point is also doubled?
A pendulum is hung in an elevator. What happens to the period of oscillation if the elevator accelerates upwards?
A pendulum is hung in an elevator. What happens to the period of oscillation if the elevator accelerates upwards?
Two charges, $q_1$ and $q_2$, are placed a certain distance apart. If the magnitude of $q_1$ is doubled and the magnitude of $q_2$ is tripled, how does the electrostatic force between them change?
Two charges, $q_1$ and $q_2$, are placed a certain distance apart. If the magnitude of $q_1$ is doubled and the magnitude of $q_2$ is tripled, how does the electrostatic force between them change?
What happens to the potential energy of a spring when it is stretched twice its original length?
What happens to the potential energy of a spring when it is stretched twice its original length?
A capacitor is charged by a battery. If the battery is disconnected and a dielectric slab is inserted between the plates, what happens to the charge on the capacitor?
A capacitor is charged by a battery. If the battery is disconnected and a dielectric slab is inserted between the plates, what happens to the charge on the capacitor?
A simple pendulum of length L has a period T. If the length is increased to 4L, the new period will be?
A simple pendulum of length L has a period T. If the length is increased to 4L, the new period will be?
The electric potential at a point due to a point charge is V. If the charge is doubled and the distance from the point is also doubled, then what will be the new potential?
The electric potential at a point due to a point charge is V. If the charge is doubled and the distance from the point is also doubled, then what will be the new potential?
Two capacitors of capacitances $C_1$ and $C_2$ are connected in series. The equivalent capacitance of the combination is?
Two capacitors of capacitances $C_1$ and $C_2$ are connected in series. The equivalent capacitance of the combination is?
Flashcards
What is Oscillation?
What is Oscillation?
A repetitive variation, typically in time, of some measure about a central value or between two or more different states.
What is Electrostatic Force?
What is Electrostatic Force?
The force of attraction or repulsion between electric charges, described by Coulomb's Law.
What is Electrostatic Potential Energy?
What is Electrostatic Potential Energy?
The energy stored in an electric field. It is related to the voltage and charge.
What is Electric Field?
What is Electric Field?
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What is Capacitance?
What is Capacitance?
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What is a Capacitor?
What is a Capacitor?
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What is an Electrical Circuit?
What is an Electrical Circuit?
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What is Electric Current?
What is Electric Current?
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What is Electrical Resistance?
What is Electrical Resistance?
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What is Voltage?
What is Voltage?
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What is Simple Harmonic Motion (SHM)?
What is Simple Harmonic Motion (SHM)?
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Study Notes
- Oscillations and Electrostatics are important topics for the MHT CET exam.
- MHT CET is a state-level entrance exam for admission to engineering and pharmacy courses in Maharashtra.
- Previous year questions from these topics can help students understand the exam pattern and difficulty level.
Oscillations
- Oscillatory motion is a repetitive variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states.
- Simple Harmonic Motion (SHM) is a special type of oscillatory motion in which the restoring force is directly proportional to the displacement from the equilibrium position and acts in the opposite direction.
- The displacement of a particle in SHM is given by x(t) = A cos(ωt + φ), where A is the amplitude, ω is the angular frequency, and φ is the phase constant.
- The period (T) of SHM is the time taken for one complete oscillation and is related to the angular frequency by T = 2π/ω.
- The frequency (f) of SHM is the number of oscillations per unit time and is the reciprocal of the period, f = 1/T = ω/(2π).
- The velocity of a particle in SHM is given by v(t) = -Aω sin(ωt + φ).
- The maximum velocity in SHM is Aω.
- The acceleration of a particle in SHM is given by a(t) = -Aω² cos(ωt + φ) = -ω²x(t).
- The maximum acceleration in SHM is Aω².
- The potential energy (U) of a particle in SHM is given by U = (1/2)kx² = (1/2)mω²x², where k is the spring constant and m is the mass.
- The kinetic energy (K) of a particle in SHM is given by K = (1/2)mv² = (1/2)mA²ω²sin²(ωt + φ).
- The total energy (E) of a particle in SHM is constant and is given by E = U + K = (1/2)kA² = (1/2)mω²A².
- A simple pendulum consists of a point mass suspended from a fixed point by a massless, inextensible string.
- The time period of a simple pendulum is given by T = 2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity.
- For small angles, the motion of a simple pendulum is approximately SHM.
- Damped oscillations are oscillations in which the amplitude decreases with time due to energy loss.
- Damping is often caused by friction or air resistance.
- Forced oscillations occur when an external periodic force is applied to an oscillating system.
- Resonance occurs when the frequency of the driving force is close to the natural frequency of the system, resulting in a large amplitude of oscillation.
Electrostatics
- Electric charge is a fundamental property of matter that causes it to experience a force when placed in an electromagnetic field.
- There are two types of electric charge: positive and negative.
- Like charges repel each other, and unlike charges attract each other.
- Charge is quantized, meaning it exists in discrete units.
- The smallest unit of charge is the elementary charge, e = 1.602 × 10⁻¹⁹ C.
- Coulomb's law states that the force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them.
- The electrostatic force between two point charges q₁ and q₂ separated by a distance r is given by F = k(q₁q₂)/r², where k is Coulomb's constant (k ≈ 8.9875 × 10⁹ N⋅m²/C²).
- The electric field (E) is the force per unit charge experienced by a test charge placed in the field.
- The electric field due to a point charge q at a distance r is given by E = k(q/r²).
- Electric field lines are used to visualize the electric field.
- Electric potential (V) is the potential energy per unit charge at a point in an electric field.
- The electric potential due to a point charge q at a distance r is given by V = k(q/r).
- The potential difference between two points is the work done per unit charge in moving a charge between the two points.
- Capacitance (C) is the ability of a body to store an electrical charge.
- A capacitor is a device used to store electrical energy.
- The capacitance of a capacitor is defined as C = Q/V, where Q is the charge stored and V is the potential difference across the capacitor.
- The capacitance of a parallel-plate capacitor is given by C = ε₀(A/d), where ε₀ is the permittivity of free space, A is the area of the plates, and d is the distance between the plates.
- The energy stored in a capacitor is given by U = (1/2)CV² = (1/2)QV = (1/2)(Q²/C).
- Dielectrics are insulating materials that can be polarized by an electric field.
- When a dielectric is inserted between the plates of a capacitor, the capacitance increases.
- The dielectric constant (κ) is the factor by which the capacitance increases when a dielectric is inserted. C' = κC
- Gauss's law states that the total electric flux through a closed surface is proportional to the enclosed electric charge.
- Electric flux (Φ) is a measure of the electric field passing through a given surface.
- Conductors are materials that allow electric charge to flow freely through them.
- Insulators are materials that do not allow electric charge to flow freely through them.
- Electric potential inside a conductor is constant.
- Electric field inside a conductor is zero in electrostatic conditions.
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