Physics Chapter on Fluid Mechanics
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Questions and Answers

What is the ratio of the heights through which the liquid will rise in the tubes?

1:2

How much energy is stored in a soap bubble of diameter 6 cm with a surface tension of 0.04 N/m?

0.9 × 10^-3 J

If two stones with radii 1:2 fall through the atmosphere, what is the ratio of their terminal velocities?

1:4

What defines the shape of the liquid meniscus when the angle of contact is obtuse?

<p>Concave shape is formed.</p> Signup and view all the answers

What is the common unit for measuring the pressure of a gas?

<p>Pascal (Pa)</p> Signup and view all the answers

What does Pascal's law of fluid pressure state?

<p>Pressure applied to an enclosed fluid is transmitted undiminished in all directions.</p> Signup and view all the answers

If a clean glass capillary tube has a radius of 0.1 mm and a surface tension of 7 x 10^-2 N/m, how high does the water rise?

<p>0.1428 m</p> Signup and view all the answers

What is the viscous force acting on a rain drop of radius 0.3 mm falling through air at terminal velocity of 1 m/s?

<p>1.017 × 10^-7 N</p> Signup and view all the answers

What is the work done in rotating an electric dipole of dipole moment $3.2 \times 10^{-8} \text{Cm}$ in an electric field of intensity $10^{4} \text{N/C}$?

<p>The work done is $6.4 \times 10^{-4} \text{J}$.</p> Signup and view all the answers

To ensure the electric potential energy of a system of charges is zero, what must the charge Q be in terms of q when three-point charges +q, +2q, and Q are placed at the vertices of an equilateral triangle?

<p>The charge Q must be $-\frac{2q}{3}$.</p> Signup and view all the answers

What expression defines the capacitance of a parallel plate capacitor with a dielectric slab inserted?

<p>The capacitance is given by $C = \frac{\varepsilon A}{d}$, where $\varepsilon$ is the permittivity of the dielectric, $A$ is the area of the plates, and $d$ is the separation between the plates.</p> Signup and view all the answers

Describe Kirchhoff's second law in terms of energy conservation.

<p>Kirchhoff's second law states that the sum of the potential differences in a closed loop must equal zero, reflecting the conservation of energy.</p> Signup and view all the answers

How can the error due to contact resistance be minimized when determining unknown resistance using a meter bridge?

<p>The error can be minimized by interchanging the positions of the known and unknown resistances.</p> Signup and view all the answers

What are beats and how are they produced when two sound waves of slightly different frequencies interfere?

<p>Beats are produced by the interference of two sound waves with slightly different frequencies, resulting in oscillations in amplitude at a frequency equal to the difference between the two frequencies.</p> Signup and view all the answers

What are the laws of vibrating strings, and how can they be verified using a sonometer?

<p>The laws of vibrating strings state that the frequency of vibration is directly proportional to the tension and inversely proportional to the length of the string. These laws can be verified using a sonometer by adjusting the tension and length and observing the resulting frequencies.</p> Signup and view all the answers

Describe the reflection of transverse waves when they encounter a denser medium.

<p>When transverse waves reflect off a denser medium, the wave inverts at the boundary. This inversion occurs because the denser medium exerts a greater restoring force.</p> Signup and view all the answers

What happens to longitudinal waves when they reflect off a rarer medium?

<p>Longitudinal waves reflect off a rarer medium without inversion, maintaining their original phase. This occurs because the rarer medium presents less resistance compared to the denser medium they originate from.</p> Signup and view all the answers

Given two vibrators with wavelengths of 2 m and 2.1 m producing 8 beats per second, how would you calculate their frequencies?

<p>The frequencies can be calculated using the relationship $v = f imes ext{wavelength}$. The velocities of both waves can be derived from their respective wavelengths and the beat frequency.</p> Signup and view all the answers

Explain the change in light speed when it travels from an optically rarer medium to a denser medium.

<p>Light speed decreases due to the change in wavelength when transitioning from a rarer to a denser medium, while its frequency remains constant.</p> Signup and view all the answers

What frequency does light with a wavelength of 5000 A.U. have when it reflects off a plane surface?

<p>The frequency of the reflected light is $6 imes 10^{14} ext{ Hz}$, calculated using the formula $f = rac{c}{ ext{wavelength}}$.</p> Signup and view all the answers

In Young's double slit experiment, how do the fringe widths differ when using green, red, and blue light?

<p>The fringe widths are largest for red light and smallest for blue light, following the order $W_R &gt; W_G &gt; W_B$, due to differences in wavelength.</p> Signup and view all the answers

What is the amplitude and period of the simple harmonic motion described with values given as 5 cm and 3.14 sec?

<p>Amplitude = 5 cm, Period = 3.14 sec</p> Signup and view all the answers

For a particle with a period of 4 seconds and an amplitude of 4 cm, how long does it take to travel 1 cm from the positive extreme position?

<p>t = 0.46 sec</p> Signup and view all the answers

Define angular simple harmonic motion and its differential equation.

<p>Angular simple harmonic motion is the rotational equivalent of linear SHM. The differential equation is given by $ rac{d^2 heta}{dt^2} + rac{g}{L} heta = 0$.</p> Signup and view all the answers

What characterizes damped oscillation in simple harmonic motion?

<p>Damped oscillation is characterized by a gradual decrease in amplitude over time due to energy loss. Factors such as friction or resistance contribute to this damping.</p> Signup and view all the answers

What is the expression for the period of a magnet performing SHM in a uniform magnetic field?

<p>The expression for the period T is given by $T = 2 au rac{m}{B^2}$, where m is the mass and B is the magnetic field strength.</p> Signup and view all the answers

What are the factors on which the total energy of a particle performing SHM depends?

<p>The total energy depends on the mass of the particle, the amplitude of motion, and the spring constant. Specifically, it is given by the equation $E = rac{1}{2} k A^2$.</p> Signup and view all the answers

What conditions must be satisfied for a standing wave on a string fixed at one end?

<p>The length of the string must be an odd integral multiple of $ rac{ ext{λ}}{4}$.</p> Signup and view all the answers

How can you derive the expression for acceleration, velocity, and displacement in linear SHM using its differential equation?

<p>The differential equation $ rac{d^2x}{dt^2} + rac{ω^2x}{0} = 0$ allows us to derive expressions: Acceleration $a = -ω^2x$, Velocity $v = ω rac{dx}{dt}$, and Displacement $x = A ext{cos}(ωt)$.</p> Signup and view all the answers

What is the SI unit of potential gradient?

<p>V/m</p> Signup and view all the answers

Which instrument measures both terminal potential difference and electromotive force?

<p>Potentiometer</p> Signup and view all the answers

What happens to the current flow when a null point is obtained in a potentiometer?

<p>Current is drawn from the main battery.</p> Signup and view all the answers

If potential gradient of a wire decreases, what happens to its length?

<p>The length increases.</p> Signup and view all the answers

In a balanced Wheatstone network, if resistances are given as 4 Ω, 8 Ω, and 12 Ω, what is the value of the unknown resistance X?

<p>24 Ω</p> Signup and view all the answers

What are the main disadvantages of a potentiometer compared to a voltmeter?

<p>A potentiometer cannot be used for measuring AC voltages and requires a zero-current condition.</p> Signup and view all the answers

What is the basis of Kirchhoff’s laws?

<p>Kirchhoff’s laws are based on the principles of conservation of charge and energy.</p> Signup and view all the answers

How do you calculate the shunt resistance required for a galvanometer?

<p>Use the formula: Shunt = G * (I_g/I_s - 1), where G is galvanometer resistance.</p> Signup and view all the answers

Define capacitive reactance.

<p>Capacitive reactance is the opposition to the flow of alternating current through a capacitor, represented as $X_C = \frac{1}{\omega C}$ where $\omega$ is the angular frequency.</p> Signup and view all the answers

What is the angular frequency of free oscillations in a circuit with a 10 microfarad capacitor and an 81 mH inductor?

<p>The angular frequency is approximately $1.1 \times 10^3$ rad/s.</p> Signup and view all the answers

State the equation for impedance Z in an A.C. circuit.

<p>The impedance in an A.C. circuit is given by $Z = \sqrt{R^2 + (X_L - X_C)^2}$, where $R$ is resistance, $X_L$ is inductive reactance, and $X_C$ is capacitive reactance.</p> Signup and view all the answers

What is the condition for current resonance in an LCR series circuit?

<p>The condition for current resonance is that the inductive reactance equals the capacitive reactance, $X_L = X_C$.</p> Signup and view all the answers

State one characteristic of a parallel LC AC resonance circuit.

<p>One characteristic is that at resonance, the total impedance is at a minimum and the circuit can draw maximum current.</p> Signup and view all the answers

What is the expression for average power consumed in a series LCR AC circuit over one cycle?

<p>The average power is given by $P = \frac{V_{rms} \cdot I_{rms}}{2} \cdot \cos \phi$.</p> Signup and view all the answers

What is the relationship between average current and rms current over half cycle?

<p>The average current is $\frac{\pi}{2} I_{rms}$.</p> Signup and view all the answers

If the peak value of an alternating emf is 15 V, what is its mean value over half cycle?

<p>The mean value over half cycle is approximately 9.548 V.</p> Signup and view all the answers

Flashcards

Simple Harmonic Motion (S.H.M.)

A periodic motion where the restoring force is proportional to the displacement from the equilibrium position, resulting in a sinusoidal oscillation.

Amplitude of S.H.M.

The maximum displacement of an object from its equilibrium position in simple harmonic motion.

Period of S.H.M.

The time taken for one complete cycle of oscillation in simple harmonic motion.

Angular S.H.M.

Simple harmonic motion where the restoring force is proportional to the angle of displacement from the equilibrium position.

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Damped Oscillation

A type of oscillation where the amplitude of oscillations gradually decreases over time due to energy dissipation.

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Standing Wave

The superposition of waves that results in a stationary pattern with fixed points of maximum and minimum amplitude.

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Wave Velocity

The speed at which a wave propagates through a medium.

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Progressive Wave

A wave that travels through a medium with a specific direction of propagation.

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Surface film

The thin layer of liquid molecules at the surface of a liquid that exhibits different properties compared to the bulk liquid due to unbalanced cohesive forces.

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Cohesive forces

Attractive forces between molecules of the same substance, holding them together.

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Liquid meniscus for obtuse angle of contact

The meniscus of a liquid will be concave, forming a dip in the center when the angle of contact between the liquid and the container is obtuse.

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Net weight of a body at terminal velocity

The net weight of a body falling with terminal velocity through a viscous medium is zero because the downward force of gravity is balanced by the upward viscous force.

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Pressure of a fluid

The pressure of a fluid is defined as the force exerted by the fluid per unit area.

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Equation of continuity

The equation of continuity states that for an incompressible fluid in steady flow, the mass flow rate is constant at any point along the flow path.

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Viscous force and velocity gradient

The viscous force experienced by a fluid is directly proportional to the velocity gradient between two parallel layers of fluid.

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Pressure gradient and viscosity

The pressure gradient within a fluid is directly proportional to the viscosity of the fluid. Higher viscosity means a steeper pressure gradient.

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Beats in sound waves

The phenomenon where two waves of slightly different frequencies interfere, producing a periodic variation in amplitude known as beats.

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Frequency of beats

The number of beats per second is equal to the difference in frequencies of the two waves.

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Beats: Amplitude variation

Whenever the crests/troughs overlap, the wave amplitude increases (constructive interference). When crests and troughs overlap, the wave amplitude decreases (destructive interference).

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Speed of light in different media

When light travels from a rarer medium to a denser medium, the speed of light decreases. This is because the wavelength of light decreases, while the frequency remains the same.

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Fringe width in Young's experiment

In Young's Double-Slit experiment, the fringe width (distance between consecutive bright or dark fringes) is inversely proportional to the wavelength of light used.

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Diffraction of Light

The bending of waves around obstacles or corners, resulting in the spreading of waves into the region behind the obstacle.

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Coherent sources of light

Two sources are coherent if they emit waves with a constant phase difference. This means the waves have a fixed relationship in their crests and troughs.

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Path difference

The path difference between two waves meeting at a point is the difference in the distances the waves travel to reach that point.

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Potential Gradient

The ratio of potential difference (voltage) to the distance over which it acts.

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Potentiometer

A device that measures the potential difference between two points in a circuit without drawing any current from the circuit.

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Null Point

The point on a potentiometer where the potential difference between the sliding contact and one end of the wire is equal to the EMF of the cell being measured.

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Current at Null Point

The current drawn from the main battery in a potentiometer setup when the null point is attained.

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Ohm's Law

The relationship between the potential difference (voltage) across a conductor and the current flowing through it, where the resistance remains constant.

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Kirchhoff's Laws

A set of rules that govern the flow of current and voltage in electrical circuits.

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Damping

The phenomenon where the amplitude of oscillations in a system decreases over time due to energy dissipation.

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DC Circuit

A type of electrical circuit where the current can only flow in one direction.

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Kirchhoff's Second Law

Kirchhoff's Second Law states that the sum of the voltage drops around any closed loop in a circuit is equal to zero. This law is based on the principle of conservation of energy, which states that energy cannot be created or destroyed.

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Minimising error in a meter bridge

The meter bridge experiment is a classic method to determine unknown resistance. When measuring the unknown resistance using a meter bridge, connecting the unknown resistance only in one gap can lead to errors caused by contact resistance at the connection points. To minimize this error, the position of the known and unknown resistances should be interchanged, as this averages out the contact resistance effects.

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Capacitance with a Dielectric

The capacitance of a parallel plate capacitor with a dielectric slab between the plates is increased by a factor of the dielectric constant of the material. The dielectric constant represents the material's ability to store more charge than air for the same applied voltage.

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Potential energy of a dipole in a field

The potential energy of a dipole in an external electric field is given by U = -p.E, where p is the dipole moment and E is the electric field strength. This means that the dipole's potential energy is minimum when it is aligned with the electric field (stable equilibrium) and maximum when it is anti-aligned with the field (unstable equilibrium).

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Electric potential of a dipole

The electric potential due to an electric dipole at a point in space is given by V = k(p.r)/r^3, where p is the dipole moment, r is the distance from the dipole to the point, and k is the Coulomb constant. The formula reflects the fact that the potential is higher closer to the dipole and decreases as the distance increases.

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Capacitive Reactance

The opposition offered by a capacitor to the flow of alternating current.

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Angular Frequency of Free Oscillations

The angular frequency at which a circuit oscillates naturally when disturbed, determined by the inductance (L) and capacitance (C).

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Impedance (Z) in an AC Circuit

The total opposition to current flow in an AC circuit, combining the effects of resistance, inductive reactance, and capacitive reactance.

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Condition for Current Resonance in an LCR Circuit

The condition in an LCR series circuit when the inductive reactance (XL) equals the capacitive reactance (XC), resulting in maximum current flow.

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Characteristic of a Parallel LC AC Resonance Circuit

In a parallel LC circuit, the impedance is maximum at resonance, making the circuit act like an open circuit.

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Average Power Consumed in an LCR AC Circuit

The average power consumed in one cycle of an LCR AC circuit is the product of the rms current, rms voltage, and the power factor.

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Relation between Average and RMS Current Over Half Cycle

The average current (Iavg) over half a cycle is related to the RMS current (Irms) by the factor of square root of 2 divided by pi.

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Mean Value of Alternating EMF Over Half Cycle

The mean value of alternating emf over half a cycle is calculated by integrating the emf function over the half cycle and dividing by the half-cycle time.

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Study Notes

Physics Question Bank 2023

  • This question bank is 100% based on the syllabus.
  • Questions are for practice only; not all will appear on the board exam.

Index of Physics Chapters

  • Rotational Dynamics (page 3)
  • Mechanical Properties of Fluids (page 7)
  • Kinetic Theory of Gases and Radiation (page 10)
  • Thermodynamics (page 13)
  • Oscillations (page 17)
  • Superposition of Waves (page 20)
  • Wave Optics (page 24)
  • Electrostatics (page 28)
  • Current Electricity (page 32)
  • Magnetic Field Due to Electric Current (page 36)
  • Magnetic Materials (page 40)
  • Electromagnetic Induction (page 44)
  • AC Circuits (page 47)
  • Dual Nature of Radiation and Matter (page 51)
  • Structure of Atoms and Nuclei (page 54)
  • Semiconductors Devices (page 59)

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