Podcast
Questions and Answers
A battery with an emf of $\epsilon$ and internal resistance r is being charged. If the charging current is i, what is the potential difference V across the battery?
A battery with an emf of $\epsilon$ and internal resistance r is being charged. If the charging current is i, what is the potential difference V across the battery?
- $V = \epsilon / ir$
- $V = \epsilon + ir$ (correct)
- $V = ir - \epsilon$
- $V = \epsilon - ir$
n identical cells, each with emf $\epsilon$ and internal resistance r, are connected in series to a load resistor R. What is the current i through the load?
n identical cells, each with emf $\epsilon$ and internal resistance r, are connected in series to a load resistor R. What is the current i through the load?
- $i = \frac{\epsilon}{R + r}$
- $i = \frac{\epsilon}{nR + r}$
- $i = \frac{n\epsilon}{R + r}$
- $i = \frac{n\epsilon}{R + nr}$ (correct)
n identical cells, each with emf $\epsilon$ and internal resistance r, are connected in parallel to a load resistor R. What is the current i through the load?
n identical cells, each with emf $\epsilon$ and internal resistance r, are connected in parallel to a load resistor R. What is the current i through the load?
- $i = \frac{\epsilon}{nR + r}$
- $i = \frac{n\epsilon}{R + r}$
- $i = \frac{n\epsilon}{nR + r}$ (correct)
- $i = \frac{\epsilon}{R + nr}$
A Wheatstone bridge is balanced. The resistances are $R_1$, $R_2$, $R_3$, and $R_4$. Which of the following equations represents the balanced condition?
A Wheatstone bridge is balanced. The resistances are $R_1$, $R_2$, $R_3$, and $R_4$. Which of the following equations represents the balanced condition?
In a meter bridge experiment, the unknown resistance X is in the left gap and a known resistance R is in the right gap. The balancing length from the left end is l. What is the value of X?
In a meter bridge experiment, the unknown resistance X is in the left gap and a known resistance R is in the right gap. The balancing length from the left end is l. What is the value of X?
A potentiometer is used to compare the emf of two cells, $\epsilon_1$ and $\epsilon_2$. The balancing lengths are $l_1$ and $l_2$ respectively. What is the relationship between the emfs?
A potentiometer is used to compare the emf of two cells, $\epsilon_1$ and $\epsilon_2$. The balancing lengths are $l_1$ and $l_2$ respectively. What is the relationship between the emfs?
Using a potentiometer, the balancing lengths for a cell is $l_1$, and with a resistance R shunted across the cell, the balancing length is $l_2$. What is the internal resistance r of the cell?
Using a potentiometer, the balancing lengths for a cell is $l_1$, and with a resistance R shunted across the cell, the balancing length is $l_2$. What is the internal resistance r of the cell?
A charged particle moves with velocity v in a region with both electric field E and magnetic field B. What is the expression for the Lorentz force F acting on the particle?
A charged particle moves with velocity v in a region with both electric field E and magnetic field B. What is the expression for the Lorentz force F acting on the particle?
A spinning skater pulls their arms inward, decreasing their moment of inertia by half. If no external torques are acting, what happens to their angular speed?
A spinning skater pulls their arms inward, decreasing their moment of inertia by half. If no external torques are acting, what happens to their angular speed?
Three objects with masses 2kg, 3kg, and 5kg are located at positions (1, 1), (2, -1), and (3, 2) in meters, respectively. What is the x-coordinate of the center of mass of this system?
Three objects with masses 2kg, 3kg, and 5kg are located at positions (1, 1), (2, -1), and (3, 2) in meters, respectively. What is the x-coordinate of the center of mass of this system?
A system consists of two particles with masses $m_1$ and $m_2$. If the velocity of the center of mass is zero, what can be said about the relationship between the momenta of the two particles?
A system consists of two particles with masses $m_1$ and $m_2$. If the velocity of the center of mass is zero, what can be said about the relationship between the momenta of the two particles?
Two particles, one with mass 1 kg and the other with mass 2 kg, are subject to external forces such that their accelerations are 2 $m/s^2$ and 1 $m/s^2$, respectively. What is the magnitude of the acceleration of the center of mass of the system?
Two particles, one with mass 1 kg and the other with mass 2 kg, are subject to external forces such that their accelerations are 2 $m/s^2$ and 1 $m/s^2$, respectively. What is the magnitude of the acceleration of the center of mass of the system?
A system of particles has a constant total momentum. Which of the following statements must be true?
A system of particles has a constant total momentum. Which of the following statements must be true?
A uniform rod of mass $M$ and length $L$ is rotating about one end with angular speed $\omega$. If no external torques are acting on the rod, and the moment of inertia is changed, which quantity remains constant?
A uniform rod of mass $M$ and length $L$ is rotating about one end with angular speed $\omega$. If no external torques are acting on the rod, and the moment of inertia is changed, which quantity remains constant?
Consider two particles of equal mass moving with velocities $v_1 = (2, 0)$ m/s and $v_2 = (0, 2)$ m/s. What is the magnitude of the velocity of the center of mass of this two-particle system?
Consider two particles of equal mass moving with velocities $v_1 = (2, 0)$ m/s and $v_2 = (0, 2)$ m/s. What is the magnitude of the velocity of the center of mass of this two-particle system?
A system of particles is known to have zero total momentum. Which of the following statements about the system's center of mass is true?
A system of particles is known to have zero total momentum. Which of the following statements about the system's center of mass is true?
A cylindrical metal rod with radius r and length L is subjected to a torsional force. Which of the following changes will result in the least change in the angle of twist, assuming the applied torque remains constant?
A cylindrical metal rod with radius r and length L is subjected to a torsional force. Which of the following changes will result in the least change in the angle of twist, assuming the applied torque remains constant?
A material has a Young's modulus (Y) of $150 \times 10^9 \frac{N}{m^2}$ and a bulk modulus (B) of $100 \times 10^9 \frac{N}{m^2}$. Calculate its Poisson's ratio ($\eta$).
A material has a Young's modulus (Y) of $150 \times 10^9 \frac{N}{m^2}$ and a bulk modulus (B) of $100 \times 10^9 \frac{N}{m^2}$. Calculate its Poisson's ratio ($\eta$).
If a material has a shear modulus (S) equal to its bulk modulus (B), what is its Poisson's ratio ($\eta$)?
If a material has a shear modulus (S) equal to its bulk modulus (B), what is its Poisson's ratio ($\eta$)?
A cube is subjected to uniform pressure on all its faces, causing a decrease in its volume. If the bulk modulus of the cube is B, and the fractional decrease in volume is $\frac{\Delta V}{V}$, what is the pressure applied?
A cube is subjected to uniform pressure on all its faces, causing a decrease in its volume. If the bulk modulus of the cube is B, and the fractional decrease in volume is $\frac{\Delta V}{V}$, what is the pressure applied?
A small metal ball is dropped into a viscous fluid. Which of the following statements accurately describes the forces acting on the ball as it accelerates downwards before it reaches terminal velocity?
A small metal ball is dropped into a viscous fluid. Which of the following statements accurately describes the forces acting on the ball as it accelerates downwards before it reaches terminal velocity?
A fluid is flowing through a pipe of non-uniform cross-sectional area. At a certain point, the area of the pipe is halved. What is the effect on the fluid velocity and pressure at that point, assuming streamline flow and negligible viscosity?
A fluid is flowing through a pipe of non-uniform cross-sectional area. At a certain point, the area of the pipe is halved. What is the effect on the fluid velocity and pressure at that point, assuming streamline flow and negligible viscosity?
Two pipes of equal length have different radii, $r_1$ and $r_2$, with $r_2 = 2r_1$. If the pressure difference across both pipes is the same, what is the ratio of the volume flow rate through pipe 2 to that through pipe 1, assuming laminar flow?
Two pipes of equal length have different radii, $r_1$ and $r_2$, with $r_2 = 2r_1$. If the pressure difference across both pipes is the same, what is the ratio of the volume flow rate through pipe 2 to that through pipe 1, assuming laminar flow?
A solid object is dropped into a fluid. The density of the object ($\rho$) is twice the density of the fluid ($\sigma$). What is the apparent weight of the object when fully submerged, expressed in terms of its actual weight (W) in air?
A solid object is dropped into a fluid. The density of the object ($\rho$) is twice the density of the fluid ($\sigma$). What is the apparent weight of the object when fully submerged, expressed in terms of its actual weight (W) in air?
A charged particle is thrown perpendicularly into a uniform magnetic field. How does the radius of the circular path change if the magnetic field strength is doubled, assuming all other parameters remain constant?
A charged particle is thrown perpendicularly into a uniform magnetic field. How does the radius of the circular path change if the magnetic field strength is doubled, assuming all other parameters remain constant?
A charged particle enters a uniform magnetic field at an angle. Which factor does NOT affect the pitch of the resulting helical path?
A charged particle enters a uniform magnetic field at an angle. Which factor does NOT affect the pitch of the resulting helical path?
In a cyclotron, what happens to the frequency of the accelerating voltage as the charged particles gain energy and their speed increases?
In a cyclotron, what happens to the frequency of the accelerating voltage as the charged particles gain energy and their speed increases?
A proton and an electron enter a uniform magnetic field with the same velocity perpendicular to the field. Which particle will have the smaller radius of curvature?
A proton and an electron enter a uniform magnetic field with the same velocity perpendicular to the field. Which particle will have the smaller radius of curvature?
A charged particle moves through a region with both electric and magnetic fields. The electric field exerts a force opposite to the magnetic force. What is the condition required for the particle to move undeflected?
A charged particle moves through a region with both electric and magnetic fields. The electric field exerts a force opposite to the magnetic force. What is the condition required for the particle to move undeflected?
Two particles with the same charge and velocity enter a uniform magnetic field. Particle A has twice the mass of Particle B. What is the ratio of the radii of their circular paths ($r_A / r_B$)?
Two particles with the same charge and velocity enter a uniform magnetic field. Particle A has twice the mass of Particle B. What is the ratio of the radii of their circular paths ($r_A / r_B$)?
A charged particle is moving in a helical path due to a uniform magnetic field. If the angle between the velocity vector and the magnetic field is increased, how will the radius of the helix change?
A charged particle is moving in a helical path due to a uniform magnetic field. If the angle between the velocity vector and the magnetic field is increased, how will the radius of the helix change?
In a mass spectrometer, ions with the same charge but different masses enter a uniform magnetic field. Which ions will complete a semi-circular path and reach the detector first?
In a mass spectrometer, ions with the same charge but different masses enter a uniform magnetic field. Which ions will complete a semi-circular path and reach the detector first?
A galvanometer with internal resistance $G$ is to be converted into an ammeter with a range of $i$, where $i_g$ is the full-scale deflection current of the galvanometer. What shunt resistance $r_g$ is required for this conversion?
A galvanometer with internal resistance $G$ is to be converted into an ammeter with a range of $i$, where $i_g$ is the full-scale deflection current of the galvanometer. What shunt resistance $r_g$ is required for this conversion?
A galvanometer with internal resistance $G$ is being used as a voltmeter. To convert the galvanometer for measuring voltage range $V$, a resistance $R$ is required to be connected in series. Which formula correctly expresses the value of $R$?
A galvanometer with internal resistance $G$ is being used as a voltmeter. To convert the galvanometer for measuring voltage range $V$, a resistance $R$ is required to be connected in series. Which formula correctly expresses the value of $R$?
A galvanometer with an internal resistance of $20 \Omega$ shows full-scale deflection at $10 mA$. What shunt resistance is needed to convert this galvanometer into an ammeter reading up to 1A?
A galvanometer with an internal resistance of $20 \Omega$ shows full-scale deflection at $10 mA$. What shunt resistance is needed to convert this galvanometer into an ammeter reading up to 1A?
A galvanometer has an internal resistance of $30 \Omega$ and requires $2mA$ for full-scale deflection. What series resistance is required to convert this galvanometer into a voltmeter reading up to 3V?
A galvanometer has an internal resistance of $30 \Omega$ and requires $2mA$ for full-scale deflection. What series resistance is required to convert this galvanometer into a voltmeter reading up to 3V?
If a galvanometer is converted into an ammeter, how does the shunt resistance affect the overall resistance and the current division in the circuit?
If a galvanometer is converted into an ammeter, how does the shunt resistance affect the overall resistance and the current division in the circuit?
If an object is taken to a height $h$ such that $h << R_e$ (where $R_e$ is the radius of the Earth), how does the acceleration due to gravity ($g_h$) at that height vary?
If an object is taken to a height $h$ such that $h << R_e$ (where $R_e$ is the radius of the Earth), how does the acceleration due to gravity ($g_h$) at that height vary?
What is the gravitational potential energy $U$ of a mass $m$ at a distance $r$ from the center of a mass $M$, assuming the reference point of zero potential energy is at infinity?
What is the gravitational potential energy $U$ of a mass $m$ at a distance $r$ from the center of a mass $M$, assuming the reference point of zero potential energy is at infinity?
A metal rod of length $L$ and Young's modulus $Y$ is suspended vertically. What is the elongation $\Delta L$ of the rod due to its own weight, if $A$ is the cross-sectional area and $M$ is the mass of the rod?
A metal rod of length $L$ and Young's modulus $Y$ is suspended vertically. What is the elongation $\Delta L$ of the rod due to its own weight, if $A$ is the cross-sectional area and $M$ is the mass of the rod?
A material undergoes a change in temperature $\Delta \theta$. If $Y$ is Young's modulus and $\alpha$ is the coefficient of linear expansion, what represents the thermal stress developed in the material?
A material undergoes a change in temperature $\Delta \theta$. If $Y$ is Young's modulus and $\alpha$ is the coefficient of linear expansion, what represents the thermal stress developed in the material?
What is the correct expression for elastic potential energy density ($U_{PH}$) in terms of stress and strain?
What is the correct expression for elastic potential energy density ($U_{PH}$) in terms of stress and strain?
If the volume of a material changes by $\Delta V$ when subjected to a pressure change $\Delta P$, what is the expression for the bulk modulus $B$?
If the volume of a material changes by $\Delta V$ when subjected to a pressure change $\Delta P$, what is the expression for the bulk modulus $B$?
A wire is twisted, and the restoring couple per unit twist is given by $\frac{\pi \eta r^4}{2L}$. Which of the following factors, when increased, would result in the least increase in the restoring couple?
A wire is twisted, and the restoring couple per unit twist is given by $\frac{\pi \eta r^4}{2L}$. Which of the following factors, when increased, would result in the least increase in the restoring couple?
Given the relationship between Young's modulus $Y$, bulk modulus $B$, and shear modulus $S$ as $Y = \frac{9BS}{3B + S}$, which of the following best describes the behavior of a material with a very large bulk modulus $B$ compared to its shear modulus $S$?
Given the relationship between Young's modulus $Y$, bulk modulus $B$, and shear modulus $S$ as $Y = \frac{9BS}{3B + S}$, which of the following best describes the behavior of a material with a very large bulk modulus $B$ compared to its shear modulus $S$?
Flashcards
Conservation of Angular Momentum
Conservation of Angular Momentum
When no external torque acts on a system, its total angular momentum remains constant.
Center of Mass (rCM)
Center of Mass (rCM)
The average position of all the mass in a system, weighted by how much mass is at each position.
rCM Formula (Discrete System)
rCM Formula (Discrete System)
rCM = (m1r1 + m2r2 + ... + mn*rn) / (m1 + m2 + ... + mn).
xCM, yCM and zCM
xCM, yCM and zCM
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Velocity of Center of Mass (vCM)
Velocity of Center of Mass (vCM)
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vCM Formula
vCM Formula
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Acceleration of Center of Mass (aCM)
Acceleration of Center of Mass (aCM)
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aCM Formula
aCM Formula
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Gravity at surface (g)
Gravity at surface (g)
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Gravity at altitude (gh)
Gravity at altitude (gh)
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gh when h << Re
gh when h << Re
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Gravity at depth (gd)
Gravity at depth (gd)
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Gravitational Potential Energy (U)
Gravitational Potential Energy (U)
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U at distance r
U at distance r
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Elongation due to weight
Elongation due to weight
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Elastic Potential Energy Density
Elastic Potential Energy Density
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Y, B, and η Relation
Y, B, and η Relation
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Y, S and σ Relation
Y, S and σ Relation
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Poisson's Ratio (η)
Poisson's Ratio (η)
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Beam Depression Formula
Beam Depression Formula
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Relative Density
Relative Density
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Gauge Pressure
Gauge Pressure
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Continuity Equation
Continuity Equation
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Bernoulli's Equation
Bernoulli's Equation
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Shunt Resistance
Shunt Resistance
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Calculating Shunt Resistance
Calculating Shunt Resistance
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Galvanometer to Voltmeter
Galvanometer to Voltmeter
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Calculating Series Resistance
Calculating Series Resistance
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Galvanometer
Galvanometer
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Path in Uniform Magnetic Field
Path in Uniform Magnetic Field
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Radius of Circular Path
Radius of Circular Path
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Time Period in Magnetic Field
Time Period in Magnetic Field
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Path at an Angle in Magnetic Field
Path at an Angle in Magnetic Field
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Radius of Helical Path
Radius of Helical Path
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Time Period of Helix
Time Period of Helix
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Pitch of Helix
Pitch of Helix
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Cyclotron Frequency
Cyclotron Frequency
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Charging Cell Voltage
Charging Cell Voltage
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Series Cells Current
Series Cells Current
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Parallel Cells Current
Parallel Cells Current
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Balanced Wheatstone Bridge
Balanced Wheatstone Bridge
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Meter Bridge Resistance
Meter Bridge Resistance
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Potentiometer EMF Ratio
Potentiometer EMF Ratio
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Potentiometer Internal Resistance
Potentiometer Internal Resistance
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Lorentz Force
Lorentz Force
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Study Notes
Chapter 1: Unit and Measurement
- Physical quantities have fundamental units like meters (m) for length, kilograms (Kg) for mass, seconds (S) for time, Ampere (A) for electric current, Kelvin (K) for temperature, Candela (Cd) for luminous intensity and Mole (mol) for the amount of substance
- Supplementary units include Radian (r) for plane angle and Steradian (Sr) for solid angle
- Distance of an object using parallax method: D = Basis / Parallax angle
- Absolute error: |Δa| = True value - Measured value
- True value, or arithmetic mean of measured values: amean = (a₁ + a₂ + ... + aₙ) / n
- Relative error in the measurement of a quantity: Δamean/amean
- Percentage error: (Δamean/amean) × 100
- Maximum permissible error in addition or subtraction: If z = A ± B, then Δz = ΔA + ΔB
- If z = (a^p * b^q) / c^r, then maximum relative error in z is calculated as: Δz/z = p(Δa/a) + q(Δb/b) + r(Δc/c)
Chapter 2: Motion in a Straight Line
- For uniformly accelerated rectilinear motion:
- v = v₀ + at (where v₀ is initial velocity)
- x = v₀t + (1/2)at² (where x is displacement)
- v² = v₀² + 2ax
- If the particle starts at x = x₀, use (x - x₀) in place of x in the equations of motion
- Relative velocity: vᴀʙ = vᴀ - vʙ (velocity of object A with respect to object B)
Chapter 3: Motion in a Plane
- Law of cosines: If R = P + Q, then R = √(P² + Q² + 2PQ cos θ), where θ is the angle between P and Q
- Direction of R: tan α = (Q cos θ) / (P + Q sin θ), where α is the angle between R and P
- Position of an object at time t: r = r₀ + v₀t + (1/2)at²
- Where r₀ is the initial position, vo is initial velocity, and a is constant acceleration
Chapter 4: Laws of Motion
- Force: F = dp/dt = m(dv/dt) + v(dm/dt)
- If mass (m) is constant: F = m(dv/dt) = ma
- Conservation of linear momentum: Σpᵢ = Σp f
- Maximum safest velocity on a level road: vmax = √(μRg), where μ is the coefficient of friction
- Maximum safest velocity on a banked road: vmax = √[Rg(μ + tan θ) / (1 - μ tan θ)]
- Angle of banking: θ = tan⁻¹(v² / rg)
Chapter 5: Work Energy and Power
- Work-energy theorem: K - Kᵢ = Wnet (change in kinetic energy equals net work done)
- Where Ki and Kf are initial, final kinetic energies, and Wnet is the net work done
- For a conservative force in 1D: F(x) = -dV(x)/dx, where V(x) is the potential energy function
- Average power: Pav = W/t (work done divided by time taken)
- Instantaneous power: P = dW/dt = F · v
- Work done by constant force: W = F · S
- Work done by multiple forces: W = Σ(Fᵢ · S) = W₁ + W₂ + W₃ + ...
- Work done by a variable force: dW = F · ds
- Relation between momentum and kinetic energy: K = p²/2m and p = √2mK (p = linear momentum)
- Potential energy:
- dU = -∫F · dr, therefore U₂ - U₁ = -∫F · dr = -W
- U = -∫F · dr
- Conservative forces: F = -U/r
- Work-energy theorem variations:
- Wc + Wnc + Wps = ΔK
- Wc = -ΔU
- Wnc + Wps = ΔK + ΔU = ΔE
- Average power (P or Pav): P = F · dS/dt = F · v = W/t
Chapter 6: System of Particles and Rotational Motion
- Perpendicular axes theorem: Iz = Ix + Iy (for moment of inertia about perpendicular axes)
- Parallel axes theorem: I = Ic + Md² (Ic is the moment of inertia about the center of mass, d is the distance)
- Moment of inertia of symmetrical bodies:
- Rod (length L, axis ⊥ to rod, center): ML²/12
- Circular ring (radius R, axis passes through center and is ⊥ to plane): MR²
- Circular ring (radius R, axis is diameter): MR²/2
- Circular disc (radius R, axis ⊥ to disc at center): MR²/2
- Circular disc (radius R, axis is diameter): MR²/4
- Hollow cylinder (radius R, axis of cylinder): MR²
- Solid cylinder (radius R, axis of cylinder): MR²/2
- Solid sphere (radius R, axis is diameter): (2/5)MR²
- Hollow sphere (radius R, axis is diameter): (2/3)MR²
- Relation between moment of inertia (I), angular momentum (L): L = Iω
- Relation between moment of inertia (I), rotational kinetic energy: K.E.rotation = (1/2)Iω²
- Relation between inertia (I) and torque (τ): τ = Iα
- Conservation of angular momentum: If no external torque acts, I₁ω₁ = I₂ω₂
- Position vector of center of mass (CM) of a discrete particle system:
- rCM = (Σmᵢrᵢ) / (Σmᵢ)
- xCM = (Σmᵢxᵢ) / (Σmᵢ), yCM = (Σmᵢyᵢ) / (Σmᵢ), zCM = (Σmᵢzᵢ) / (Σmᵢ)
- Velocity of center of mass: vCM = (Σmᵢvᵢ) / (Σmᵢ)
- Acceleration of CM: aCM = (Σmᵢaᵢ) / (Σmᵢ)
- Momentum of system: P = Σpᵢ = (Σmᵢ) vCM
- Center of mass of continuous mass distribution: -rCM = (∫r dm) / dm, xCM = (∫x dm) / dm, yCM = (∫ydm) / dm, zCM = (∫z dm) / dm
- Center of mass locations of common objects:
- Uniform rod of length L: xCM = L/2, yCM = 0, zCM = 0
- Uniform semicircular ring of radius R: xCM = 0, yCM = 2R/π, zCM = 0
- Uniform semicircular disc of radius R: xCM = 0, yCM = 4R/3π, zCM = 0
- Uniform quarter of a ring of radius R: xCM = 2R/π, yCM = 2R/π, zCM = 0
- Uniform quarter of a disc of radius R: xCM = 4R/3π, yCM = 4R/3π, zCM = 0
- Uniform spherical shell of radius R: xCM = 0, yCM = R/2, zCM = 0
- Uniform spherical of radius R: xCM = 0, yCM = 3R/8, zCM = 0
Chapter 7: Gravitation
- Newton's universal law of gravitation: F = G(m₁m₂) / r²
- In vector form: F = [G(m₁m₂) / r²]⋅ r̂
- Kepler's II law: dA/dt = L/2m (areal velocity is constant)
- Kepler's III law: T² α R³
- Gravitational acceleration:
g = GM / R² - Variation of g at altitude 'h': gh = g[R / (R + h)]²
- If h << R: g_h ≈ g[1 - (2h / R)]
- Variation of g at depth 'd': gd = g[1 - (d / R)]
- Gravitational potential energy: U = WAB = -G(Mm/r)
Chapter 8: Mechanical Properties of Solids
- Elongation produced in rod of length L due to its own weight: ΔL = (ρgL² / 2Y) = MgL/2AY
- Thermal Stress: Y α Δθ
- Elastic potential energy: U =(1/2) x stress x strain
- Bulk modulus: B = -V (ΔP / ΔV)
- Compressibility: 1/B
- Restoring couple per unit twist: (πnr⁴)/2l
- Strain: σ = (Δr/r) / (ΔL/L)
- Relations between elastic constants:
- Y = (9BS) / (3B + S)
- Y = 3B(1 - 2η)
- Y = 2S(1 + σ)
- Poisson's Ratio: η = (3B - 2S) / (6B + 2S)
- B = (2S(1 + η)) / (3(1 - 2η))
- Depression at the middle of a beam = (Wl³) / (4Ybd³)
- Sheer Modulus S = (Fh) / (Ax)
Chapter 9: Mechanical Properties of Fluids
- Relative density (ρrel): ρsubstance / ρwater (at 4°C)
- Gauge pressure (Pg): ρgh
- Apparent weight (W') of a body in fluid: W' = W(1 - ρ/σ) where W = weight in air
- Equation of continuity: Av = constant (A = area, v = velocity)
- Bernoulli's equation: P + ρgh + (1/2)ρv² = constant
- Coefficient of viscosity (η): (Fl)/vA (F = viscous force, l = separation, A = area, v = velocity)
- Stokes' law: F = -6πηav (for viscous force on a sphere)
- Terminal velocity (VT): (2a²(ρ - σ)g) / 9η (a = radius, = density of falling body, = density of fluid)
- Reynolds number (Re): (ρvd) / η (d = diameter of pipe)
- Excess pressure inside a liquid drop: P_i - P_o = 2S / R
- Excess pressure inside an air bubble: P_i - P_o = 4S / R
- Height in a capillary tube: h = (2S cos θ) / (rρg)
Chapter 10: Thermal Properties of Matter
- Temperature conversion:
- °C ↔ °F: tc = (5/9)(tF - 32), tF = (9/5)tc + 32
- °C ↔ K: T = tc + 273.15, tc = T - 273.15
- °F ↔ K: tF = (9/5)T - 459.67, T = (5/9)tF + 255.37
- Relationships between linear, area, volume expansion: β = 2α, γ = 3α
- Heat flow: Q = (kA(T₁ - T₂)t) / x
- Heat current: H = dQ/dt = -kA(dT/dx)
- Coefficient of reflectivity (r): Q₁/Q
- Coefficient of absorptivity (a): Q₂/Q
- Coefficient of transitivity (t): Q₃/Q
- Newton's law of cooling:
- ln[(T₁ - T₀) / (T₂ - T₀)] = Kt
- (T₁ - T₂) / t = K[ (T₁ + T₂) / 2- T₀]
Chapter 11: Thermodynamics
- First law of thermodynamics: ΔQ = ΔU + ΔW
- Work done: ΔW = PAV therefore, ΔQ = ΔU + PAV
- Relation between specific heats: Cp - Cv = R
- Isothermal process: PV = constant
- Also, V ∝ T and P∞ T (Charles's Law)
- Refrigerator:
- B = Q2/(Q1-Q2)
- Also, efficiency = 1/B
Chapter 12: Kinetic Theory of Gases
- Ideal Gas Equation: PV = uRT
- Pressure exerted by ideal gas: P=(1mMv^2)/ 3V
Chapter 13: Ocsillations
- SHM for displacement: x= A sin(wt + O)
- Velocity of SHM Formula: v= Aw cos ot
- Energy in SHM:
- Potential Energy: U= 1/2mw^2x^2
- Kinetic Energy: K= 1/2mw^2(A^2-x^2)
Chapter 14: Waves
- Plane of a Progressive harmonic wave
- y(x,t)= a sin (kx-ot+0)
- Transerve wave on a stretched string
Chapter 15 : Electric charges and fields
-
the amount of electrostatic force is indicated in Newtons (N). F = kq1q2 / r^2
-
= q.E where E = q / (4περR2 ) is the electric field because of charge Q2.
Chapter 16 : Electostatic pottential and capacitance
Where, Capacitance= C = ε0A* d Electric feild energy: (a) U = 1/2 Qv = Q^2 / 2C = 1/2 CV^2
Chapter 17: Current Electricity
-
Conductance = G= 1/R
-
According to the law of "OHMS" J= OV and I= IR
Chapter 18 : Moving charges and magnitic Field
-
Moving electric field:
-
B = Ho I/ 2R
Chapter 19: Magnetism and Matter
Bar magnet: the electrostatic Analog
Chapter 20 : Electromagnetism and Matter
average induced equation:
- = (E) = -(02-01 / T2-T1
Chapter 21 : Electromagnetomic Waves equations
- 0 Eo^2 = C B2 /Mo B
Chapter 22 : Ray optics and Optical insturments
- Mirror equation -1/v + 1/u= 1/f where “YOU” refering to “u” as an (object distance) , Image Distance : “v” ,and Length of Focal : “f- length” :
- 2F= R.
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