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Q.2 Answer the following questions
Chapter 1. Rotational dynamics
Q. 1. State the relation between the linear velocity and the angular velocity of a particle in circular motion.
\vec{n} \vec{m}\times\vec{r} Ans. Linear velocity, =where is the angular velocity and is the radius vector.
At every instant, magnitude e~v=col . \overline{v} \vec{\phi} and are mutually perpendicular, so that in
Q. 2. What can you say about the angular speed of an hour hand as compared to that of the Earth's rotation about its axis?
Ans. The periods of rotation of an hour hand and the Earth are and T_{E}=24~h , respectively, so that their angular speeds are = and og =\frac{2\pi}{24}rad/h. T_{h}=12h
radh
ch=2co_{5}
School
Q. 3. What is the angle between linear acceleration acceleration of a particle in nonuniform circular motion? and angular
Ans. The angular acceleration in a nonuniform circular motion is an axial vector, perpendicular to the plane of the motion. The linear acceleration is in the plane of the motion. Hence, the angle between them is 90°.
Q. 4. State any two quantities that are uniform in UCM.
Ans. Linear speed and angular velocity. (Also, kinetic energy, angular
speed and angular momentum.)
[Note: Linear velocity, acceleration, momentum and centripetal force are nonuniform in UCM.]
Q. 5. The equations of motion of a particle of mass m in circular motion with constant angular speed @are x=rcos of and y= r sin ot. Write the expression for the force on the particle.
Ans. The particle is performing UCM with radius vector 60/444 = r(cos ori + sin orj). Since a², the force on the particle is F=ma-mor (cos ori + sin orj).
Q. 6. Why is centrifugal force called a pseudo force?
Ans. A force which arises from gravitational, electromagnetic or nuclear interaction between matter is called a real force. The centrifugal force does not arise due to any of these interactions. Therefore, it is not a real force.
The centrifugal force in the noninertial frame of reference of a particle in circular motion is the effect of the acceleration of the frame of reference with respect to an inertial frame of reference. Therefore, it is called a pseudo or fictitious force.
Q. 7. Why is the work done by a centripetal force equal to zero? est
Ans. The centripetal force F and linear velocity 7 of a particle in circular motion are perpendicular to each other at every instant, the force being radially inward and velocity tangential. Therefore, F=0 at every instant. Since ds/dt, the work done by the centripetal by the cer W=Fds=Fdt = 0. force,
Q. 8. Why does a motorcyclist moving along a level curve at high
speed have to lean more than a cyclist moving along the same curve at
low speed?
Ans. A two-wheeler, in moving along a level curve of radius r
with speed v, must lean at an angle with respect to the vertical, where 0-tan 12. Therefore, for a given r, 0 should be more, for higher v. rg
Q. 9. A small body of mass m is tied to a string and revolved in a vertical circle of radius r. If the tension in the string at the highest point is mg, what is its speed there?
Ans. If ₁ is the speed and T_{1} the tension in the string at the highest point, T₁ = mg = mo mg
0=2rg2rg
Q. 10. How does the normal reaction on a car crossing over a convex bridge vary with speed?
Ans. Suppose a car of mass m, travelling with a uniform speed v crosses over a bridge which is in the form of a convex arc of radius r. The forces acting on the car at the highest point are (i) the normal reaction \vec{N} vertically upward (ii) the gravitational force m\vec{g} vertically downward. Their resultant mg-N provides the centripetal force N=m(g-\frac{v^{2}}{r}) which shows that as increases, N decreases. mg-N=\frac{mv^{2}}{r}
Q. 11. Why is it useful to define radius of gyration?
Ans. The radius of gyration of a body of mass M and moment inertia / is k=\sqrt{I/M} Thus, the radius of gyration is less if / is less, i.e., if the mass is distributed close to the axis; and it is more if I is more, i.e., if the mass is distributed away from the axis. Thus, it gives the idea about the distribution of mass about the axis of rotation.
Best
Q. 12. State the formula for the moment of inertia of a solid sphere about an axis passing through its centre. (Sept. '21)
Ans. The MI of a uniform solid sphere of radius R and mass M about
an axis passing through its centre (i.e., about a diameter) is
I_{CM}=\frac{2}{5}MR^{2}
Q. 13. State the expression for the MI of a thin spherical shell (i.e., a thin-walled hollow sphere) about its diameter. Hence obtain the expression for its MI about a tangent.
Ans. The MI of the thin spherical shell of radius R and mass M about its diameter is I_{CM}=\frac{2}{3}MR^{2}
Let I be its MI about a tangent parallel to the diameter. Here, h = R = distance between the two axes. Then, according to the theorem of parallel axis,
I=I_{CM}+Mh^{2}
=\frac{2}{3}MR^{2}+MR^{2}=\frac{5}{3}MR^{2}
Q. 14. A uniform disc and a hollow right circular cone have the same formula for moment of inertia for rotation about their corresponding central symmetry axes. Why is it so?
Ans. The moment of inertia of a hollow right circular cone about its central symmetry axis is\frac{1}{2}MR^{2} the same as that of a disc about its transverse symmetry axis. This is because the distribution of mass of the hollow cone about its central symmetry axis is the same as that of a disc.
Q. 15. Show that the square of the radius of gyration of a hollow cylinder is twice that of a solid cylinder having the same radius for rotation about the respective cylinder axis.
gest
Ans. For rotation about the cylinder axis, the moments of inertia
(1) a thin hollow cylinder I_{HC}=Mk_{HC}^{2}=MR^{2}
(2) a solid cylinder, I_{SC}=Mk_{SC}^{2}=\frac{1}{2}MR^{2}
School
k_{HC}^{2}=R^{2}=2k_{SC}^{2}
Q. 16. Find the ratio of the radii i of gyration of a circular disc and a circular ring of the same radii about a tangential axis in their planes. of gyra
Ans. For rotation about a tangent in its plane, the radius of gyration of
(1) a disc, k_{disc}=\frac{\sqrt{5}}{2}R
(2) a ring. k_{ring}=\sqrt{\frac{3}{2}}R
\frac{k_{disc}}{k_{ring}}=\frac{\sqrt{5}}{2}\times\sqrt{\frac{2}{3}}=\sqrt{\frac{5}{6}}
Q. 17. What happens when a ballet dancer stretches her arms while taking turns?
Ans. When a ballet dancer stretches her arms in a dance spin, her moment of inertia increases. Consequently her angular speed decreases to
conserve angular momentum. This reduces the linear speed of an ice ballet dancer to prevent skidding while taking turns of larger radius.
Q. 18. If the Earth suddenly shrinks, mass remaining constant, what will be the effect on the duration of the day?
Ans. If the Earth suddenly shrinks, mass remaining constant, the moment of inertia of the Earth will decrease, and consequently the angular velocity of rotation about its axis will increase. Since period Toc duration of the day I will decrease. 1 the
Q. 19. A ring and a disc at rest on an inclined plane roll down through the same height. Compare their speeds at the bottom of the incline.
Ans. In the usual notation,
disc
(4/3) gh
Vring
√gh
3
Chapter 2. Mechanical properties of fluids
Q. 20. What is an incompressible fluid?
Ans. An incompressible fluid is one which does not undergo change in volume for a large range of pressures. Thus, its density has a constant value throughout the fluid. In most cases, liquids are incompressible.
Q. 21. State any two applications of Pascal's law.
Ans. Applications of Pascal's law:
(1) Hydraulic car lift and 1 hydraulic press
(2) Hydraulic brakes.
Q. 22. What is meant by a surface film?
Ans. The layer of the liquid surface of thickness equal to the range of molecular attraction is called a surface film.
Q. 23. State the CGS and SI units of surface tension.
Ans. CGS unit of surface tension: The dyne per centimetre (dyn/cm) or, equivalently, the erg per square centimetre (erg/cm²).
SI unit of surface tension: The newton per metre (N/m) or, equivalently, the joule per square metre (J/m²)
Q. 24. Obtain the dimensions of surface tension.
Ans. Surface tension is a tangential force per unit length.
.. [Surface tension] = [force] [MLT-2] [MLT-2] [length] = [M°L'T']
Q. 25. State the dimensions and SI unit of surface ene
Ans. Dimensions: [surface energy] = [ML2T-2] SI unit: the joule (J).
Q. 26. Write the expression for the angle of contact in terms of interfacial tensions.
Ans. The angle of contact for a liquid-solid pair, 0 = cos T where T₁ = the liquid-solid interfacial tension, 7, the solid-gas (air +
vapour) interfacial tension, 73 = the liquid-gas interfacial tension.
Q. 27. In terms of interfacial tensions, when is the angle of contact acute?
Ans. The angle of contact is acute when the solid-gas (air + vapour interfacial tension is greater than the liquid-solid interfacial tension.
[Note: The angle is obtuse when the latter is greater.]
Offerten Digest
Q. 28. Why is cold wash recommended for new cotton fabrics while hot wash for removing stains?
Ans. Cold wash is recommended for new/coloured cotton fabrics. Cold water, due to its higher surface tension, does not penetrate deep into the fibres and thus does not fade the colours. Hot water, because of its new/coloure lower surface tension, can penetrate deep into fabric fibres and remove tough stains.
Q. 29. What is the effect on the surface tension of (i) molten copper (ii) molten cadmium on increasing its temperature?
Ans. The surface tension of (i) molten copper (ii) molten cadmium increases on increasing its temperature.
Q. 30. What is meant by a steady flow?
Ans. When a liquid flows slowly over a surface or through a pipe such that its velocity or pressure at any point within the fluid is constant, it is said to be in steady flow.
Q. 31. State the formula for critical velocity for fluid flow in terms of Reynolds number.
(March '22)
Ans. For a given system geometry, the free stream velocity of a fluid, of density p and coefficient of viscosity n, beyond which a streamline flow becomes turbulent is called the critical velocity given by 65/444 Re Vcritical =
pd
where d is some characteristic dimension of the system and Re is the critical Reynolds number.
Q. 32. What is viscous drag?
Ans. When a fluid flows past a solid surface, or when a solid body
moves through a fluid, there is always a force of fluid friction opposing the motion. This force of fluid friction is called the drag force or viscous drag.
Q. 33. Explain why flow speed is greatest where streamlines are closest together.
Ans. By the equation of continuity, the flow speed is inversely proportional to the area of cross section of a flow tube. Where the area of cross section is small, i.e., streamlines are close, the flow speed is large and
vice versa.
Chapter 3. Kinetic theory of gases and Radiation
Q. 34. What will happen to the mean square speed of the molecules of a gas if the temperature of the gas increases?
Ans. If the temperature of a gas increases, the mean square speed of the molecules of the gas will increase in the same proportion.
Q. 35. How does the kinetic theory of gases justify the increase in the temperature of a gas when heated?
Ans. Molecules of a gas possess kinetic energy and are in a state of continuous random motion. The average kinetic energy per molecule being proportional to the absolute temperature of the gas, the temperature of the
gas increase on heating.
Q. 36. Two different pure gases have the same temperature. Do their molecules have the same rms speeds?
Ans. The rms speed of a gas molecule, Urms C T Mo where T is the
absolute temperature and Mo is the molar mass. Since, two different pure gases differ in their molar masses, their rms speeds at the same temperature T are different.
Q. 37. State the types of degrees of freedom of non-rigid diatomic molecules.
Ans. A soft or non-rigid diatomic molecule has three translational degrees of freedom, two rotational degrees of freedom and one vibrational degree of freedom.
Chapter 4. Thermodynamics
Q. 38. Give an example of some familiar process in which no heat is added to or removed from a system, but the temperature of the system changes.
Ans. A free expansion is an adiabatic process in which the temperature of the gas changes although no heat is added to or removed from the system (gas).
Q. 39. Give an example of some familiar process in which heat is added to an object, without changing its temperature.
Ans. (i) Melting of ice (ii) Boiling of water.
Q. 40. A gas contained in a cylinder surrounded by of insulating material is quickly compressed. (a) Has there been a transfer of heat? (b) Has work been done? cho Digest y a thick 1 thick layer
Ans. (a) There is sno transfer of heat. (b) The work is done on the gas.
Q. 41. What is mechanical equilibrium?
(March '22)
Ans. A system is said to be in mechanical equilibrium when there are no unbalanced forces within the system and between the system and its
surroundings.
OR
A system is said to be in mechanical equilibrium when the pressure in the system is the same throughout and does not change with time.
Q. 42. What is thermal equilibrium?
(March '22)
Ans. A system is in a state of thermal equilibrium if there is no net transfer of heat between the various parts of the system or between the system and its surroundings, so that the temperature remains constant and uniform throughout the system.
(Sept. '21)
Q. 43. What is an isothermal process?
Ans. A process in which changes in pressure and volume of a system take place at a constant temperature is called an isothermal process.
Q. 44. Give two examples of an irreversible process.
Ans. Examples of an irreversible process: (1) Free expansion of a
gas (2) All chemical reactions (3)Diffusion~o two dissimilar inert gases (4) A gas seeping through a porous plug.
Q. 45. What is a heat engine?
Ans. A heat engine is a device which takes a system through a repeated thermodynamic cycle that converts part of the heat supplied by a hot reservoir into work (mechanical energy) and releases the remaining part to a cold reservoir. At the end of every cycle, the system is returned to the initial state.
Q. 46. What are the two basic types of heat engines?
Ans. Types of heat engines: (i) External combustion engine - in
which the working substance is heated externally, as in a steam engine.
(ii) Internal combustion engine-in which the working substance heated internally, as in a petrol engine or diesel engine. Digest
Q. 47. What is a refrigerator?
Ans. A refrigerator is a device that uses work to el in the form of heat from a cold reservoir to a hot eservoir as it continuously repeats a thermodynamic cycle. Thus, it is a heat engine that runs in the backward direction.
Q. 48. What sets the limit on the efficiency of a heat engine?
Ans. The efficiency of a heat engine, given by \eta=1-\frac{T_{C}}{T_{H}}, shows
that the efficiency is limited by the temperature of the cold reservoir; Tc; T_{u} is the temperature of the hot reservoir. For maximum efficiency, T_{c} should be as low as possible and T_{H} should be as high as possible.
Chapter 5. Oscillations
Q. 49. Spring constant is a dimensional constant. Justify.
Ans. Since restoring force, F=-kx the spring constant k has the dimensions of F/x. Since F and x have different dimensions, k is a dimensional constant.
Q. 50. How does the frequency of an SHM vary with the force constant k?
Ans. The frequency of a particle of mass m performing SHM is \frac{1}{n} k foc√k f=
Thus, the frequency of an SHM is directly proportional to the square root of the force constant of the motion.
Q. 51. At which position is the restoring force acting on a particle executing linear SHM maximum?
Ans. In linear SHM, F|oc|x.
(Sept. '21)
|F|=F_{max} when |x|=x_{max}=A , where A is the amplitude of SHM.
Q. 52. The period of oscillation of a body of mass m_{1} suspended from a light spring is T. When a body of mass m_{2} is tied to the first body and the system is made to oscillate, the period is 27. Compare the masses m₁ and m2.
m
2T =2= T
Ans. T=2π m₁+m₂ m m
m2
Digest
\frac{m_{1}+m_{2}}{m_{1}}=4 \therefore\frac{m_{2}}{m_{1}}=\frac{3}{1} This gives the required ratio of the masses.
a^{\circ}
Q. 53. In linear SHM, what is the phase difference between (i) displacement and acceleration (ii) the velocity city and acceleration? the
Ans. (i) id(ii)\frac{\pi}{2}rad.
M.S.N
[Note: The phase differences are independent of the initial phase.]
Q. 54. State the expression for the total energy of SHM in terms of acceleration.
Ans. The total energy of a particle of mass m performing SHM with angular frequency, E=\frac{1}{2}m\omega^{2}A^{2}
The maximum acceleration of the particle, a_{max}=\omega^{2}A E=\frac{1}{2}mAa_{max} is the required expression.
Q. 55. Under what conditions can we consider the oscillations of a simple pendulum to be linear simple harmonic?
Ans. The oscillations of a simple pendulum are approximately linear simple harmonic only if
(i) the amplitude of oscillation is very small compared to ( 69/444 \hat{\cdot}
ii) the oscillations are in a single vertical plane.
Q. 56. State explaining each term in the differential equation of angular oscillations of a bar magnet in the Earth's magnetic field.
Ans. For a bar magnet of magnetic moment u suspended horizontally in the Earth's magnetic field B_{h} and set into small torsional oscillations in a horizontal plane, the equation of motion is \frac{d^{2}\theta}{dt^{2}}+\frac{\mu B_{h}}{I}\theta=0 where \alpha=\frac{d^{2}\theta}{dt^{2}}= the angular acceleration and I=tt moment of inertia of the magnet about the axis of oscillation which is a transverse symmetry axis of the bar magnet.
Digest ``_{22}
Q. 57. Write the differential equation for angular SHM.
Ans. For small torsional oscillations of a body of moment of inertia / suspended by a wire/fibre of torsion constant c, the differential equation of angular SHM is I\frac{d^{2}\theta}{d\epsilon^{2}}+c~\theta=0 where \frac{d^{2}\theta}{dt^{2}}=\alpha is the angular the body when its angular displacement from the rest position acceleration MSC ferential is 0.
Q. 58. Write the differential equation of damped oscillations of a body in the presence of a resistive force directly proportional to the velocity.
Ans. In the presence of a resistive force f=-\beta v, where ẞ is the damping constant and is the velocity, the differential equation of an oscillator of mass m and force constant k is m\frac{d^{2}x}{dt^{2}}+\beta\frac{dx}{dt}+kx=0.
Q. 59. A wave is represented by an equation y = A sin (Cx+Bt). Given that the constants A, B, C are positive, in which direction the wave is travelling?
Ans. The wave is travelling along the negative x-direction.
Q. 60. A simple harmonic progressive wave is given by
y = sin (kx-ot). What is (i) the particle velocity at a point x and time t (ii) the wave speed?
Ans. (i) Particle velocity, dy dt A cos(kx-ot) (ii) Wave speed,
k
Q. 61. What happens to a particle velocity when a transverse wave is reflected from (i) a rarer medium (ii) a denser medium?
Ans. When a transverse wave is reflected from a rarer medium or a denser medium, there is no change of phase in either case so that there is no change of the particle velocity.
Q. 62. What happens to a particle velocity, when a sound wave is reflected from (i) a rarer medium (ii) a denser medium?
Ans. When a sound wave is reflected from a rarer medium, there is change of phase so that there is no change of the particle velocity. there is n Digest no
When a sound wave is reflected from a denser medium, there is change of phase of 180° or a radians so that the particle velocity is reversed.
Q. 63. Two interfering waves of the same frequency are out of phase but have different amplitudes A, and A₂. What can you say about the intensity of the resultant wave?
Ans. The two interfering waves are out of phase. Thus, the amplitude and hence the intensity of the resultant wave is minimum, Imin (Amin)2 where (Amin)²= (A1-A2).
Q. 64. A tuning fork is in resonance with a closed pipe. But the same tuning fork cannot be in resonance with an open pipe of the same length. Why?
Ans. For the same length of air column, and the same speed of sound, the fundamental frequency of the air column in a closed pipe is half that in an open pipe. Hence, a tuning fork in unison with the air column in a
closed pipe cannot be in unison with the air column of the same length in an open pipe.
Q. 65. For a stationary wave set up in a string having both ends fixed, what is the ratio of the fundamental frequency to the second harmonic?
Ans. The fundamental is the first harmonic. Therefore, the ratio of the fundamental frequency (n) to the second harmonic (n) is 1: 2.
Chapter 7. Wave optics
Q. 66. A parallel beam of monochromatic light in vacuum (medium 1) is incident normally on the plane surface of a medium 2. What happens to the wavelength and frequency of the light in medium 2?
Ans. The frequency of a wave remains unchanged as it passes from one medium to another. The speed of light in medium 2 being less than its speed in vacuum (medium 1), its wavelength in medium 2 is less than that in vacuum.
Q. 67. What is meant by polarized light?
Ans. If the vibrations of the electric field E in a light wave are to a single plane containing the direction of propagation, the light wave is said to be plane-polarized light or linearly polarized light. hool confined
Q. 68. What is a polarizer?
Ans. A material or device which allows only only those light waves to pass through undiminished (almost) which have their electric field E, in a particular plane (transmission axis) is called a polarizer. For waves with the electric field in other directions, the component of E, parallel to the transmission axis is allowed to pass while the component perpendicular to that axis is completely blocked.
Q. 69. Give a common use of a polarizer.
Ans. Polaroid sunglasses and filter for camera lens are used to reduce or eliminate intense reflected light from reflective nonmetallic surfaces like
glass, rock faces, roadways and water.
Q. 70. Unpolarized light is passed through two polarizers.
Under what condition is the intensity of the emergent light
(i) maximum (ii) zero?
Ans. Let be the angle between the axes of polarization of a pair of polarizers. When an unpolarized light beam is passed through the polarizers, the intensity of emergent light is
(i) maximum for 0=0°
(ii) minimum (equal to 0) for 0-90°.
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Q. 71. What are crossed polarizers?
Ans. Crossed polarizers are a pair of polarizers with their transmission axes perpendicular to each other so that the transmitted light intensity is zero.
Q. 72. How is Young's interference experiment performed using a single source of light?
Ans. When a narrow slit is placed in front of an intense source of
monochromatic light, cylindrical wavefronts propagate from the slit. In Young's experiment, two coherent sources are then obtained by wavefront splitting by placing a second screen with two narrow slits at a small distance from the first slit.
Q. 73. In Young's double-slit experiment, if the path differences at a certain point of the screen is 2.999, what can you say about the intensity of light at that point?
Ans. As the path difference is 2,999% 3-an integral multiple of , the intensity of light at that point will be nearly maximum and the point will be very close to the centre of the third bright fringe.
Q. 74. In Young's double-slit experiment, the slit separation is d and the slit-to-screen distance is D. If the second minima in the interference pattern are formed exactly in front of the two slits, what is the wavelength of the light used?
Ans. The distance of an mth minimum from the central fringe is D 2 d y=(2m-1)
Given that for d t for m = 2, y2= 2
(4-1)/2= d
Then, the wavelength of the light used is 2 = d 3D
Ans. In Fresnel diffraction, either the source of light or the screen or both are at finite distances from the diffracting aperture.
Q. 76. What is Fraunhofer diffraction?
Ans. In Fraunhofer diffraction, both the source and the screen are at infinite distances from the aperture. This is achieved by placing the source at the focus of a convex lens and the screen at the focal plane of another convex lens.
Q. 77. What should be the order of the size of an obstacle or aperture to produce diffraction of light?
Ans. For pronounced diffraction, the size of an obstacle or aperture should be of the order of the wavelength of light or greater.
Q. 78. State the condition (Abbe's condition) for the least distance between two illuminated objects so that they are just resolved when they are viewed through a microscope.
Ans. When two point objects illuminated by the same source are viewed through a microscope, the least separation between the objects such that they are just resolved, according to Abbe, is
dmin =
where is the wavelength of light, n is the refractive index of the medium between the objects and the objective lens, 2imax is the angle of maximum cone of light incident on the lens. The product n sin imax is a characteristic of a given objective lens and is called the numerical aperture; dmin is the limit of resolution. School called
2n sin imax
Dig
power Q. 79. How can the resolving power of a telescope be increased?
Ans. The resolving power of a telescope depends directly on the diameter of the objective lens or mirror, and inversely on the wavelength of radiation. Hence, the resolving power can be increased by
(1) using an objective lens/mirror of larger diameter
(2) observing a celestial object at smaller wavelengths.
Chapter 8. Electrostatics
Q. 80. Does the electric flux due to a point charge enclosed by a spherical Gaussian surface change when the radius of the Gaussian surface is increased? Why?
Ans. No. Electric flux, or the number of electric field lines, passing through the Gaussian surface is independent of the size of the Gaussian surface and depends on the number of field lines originating from or terminating at the point charge, which in turn depends on the magnitude of the point charge and the permittivity of the medium.
Q. 81. For a charged cylindrical conductor of cross-sectional radius R, what is the relation between the surface charge density and linear charge density?
Ans. Surface charge density, a = where is the linear charge 2π' density.
Q. 82. Acharge q is moved without acceleration from a point A above a dipole of dipole moment p to a point B below the dipole in the equatorial plane. Find the work done in this process.
A
B
Ans. The equatorial plane of an electric dipole is an equipotential with V= 0. Therefore, no work is done in moving a charge between two points in the equatorial plane of a dipole.
Q. 83. What is the shape of equipotential surfaces in a uniform electric field? hool Digest
Ans. In a uniform electric field, the field lines are equally-spaced parallel lines and the equipotential surfaces are parallel planes perpendicular to the field lines. For equal potential differences between adjacent planes, these equipotentials are equally spaced.
Q. 84. What is the potential energy of a point charge in an external electric field?
Ans. Consider a charge q placed in an external electric field at a point whose position vector with respect to an arbitrary reference frame is r. If V(7) is the potential of the point, with respect to an arbitrary reference zero at infinity, then the potential energy of the charge q at the point is
U(F)=qV(F)
where it is assumed that q is sufficiently small and does not significantly distort the electric field and the potential at the point.
Q. 85. If the difference between the radii of the two spheres of a spherical capacitor is increased, state whether the capacitance will increase or decrease.
C= 4πέρ
ab
Ans. The capacitance of a spherical capacitor is
b-a
where a and b are the radii of the concentric inner and outer conducting shells. Hence, the capacitance decreases if the difference b- 75/444
Q. 86. What are the functions of a dielectric in a capacitor?
Ans. A dielectric material between the plates of a capacitor (i) increases the capacitance of the capacitor (ii) provides mechanical support to the plates (iii) increases the maximum operating voltage, i.e., the maximum voltage to which the capacitor may be charged without breakdown of the insulating property of the medium between the plates.
Chapter 9. Current electricity
Q. 87. What is a potentiometer?
Ans. A potentiometer is an instrument for measuring, comparing or dividing small potential differences. It consists of a long and uniform resistance wire along which a potential gradient is set up by connecting a cell of extremely stable emf connected across its ends.
Q. 88. Define potential gradient along a wire.
Wire (March 2 Ans. Potential gradient along a (potentiometer) wire is the potential difference (the fall of potential from the high potential end) per unit length of the wire.
Q. 89. On what factors does depend? : the potential potential gradient of the wire foes the pote
Ans. The potential gradient depends upon the potential difference between the ends of the wire and the length of the wire.
Q. 90. What will be the effect on the position of null point on a potentiometer wire if the current through the wire is decreased?
Ans. The potential gradient along a potentiometer wire is directly proportional to the current through the wire and the null length on a potentiometer is inversely proportional to the potential gradient. Hence, the potential gradient decreases with a decrease in the current. Consequently, the null length will decrease.
