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The entropy of a system, S, is related to the accessible phase space volume G by S = kBlnG(E, N, V) where E, N and V are the energy, number of particles and volume respectively. From this one can conclude that G
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 1
Two macroscopic system, which are in thermal contact, the required condition for the equilibrium is that their b parameter must be equal.
accessible phase space volume
S = klnr(E,V,N)
and it is obvious that at equilibrium the accessible phase volume is maximum.
Let dw be the work done in a quasistatic reversible thermodynamic process. Which of the following statements about dw is correct?
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 2
The first law of thermodynamics can be given
dQ = dU + dW
here dQ and dW both are path function and dU is state function. For making dW a perfect differential, we take dQ = 0
So dU + dW = 0
dW = -dU
and dQ = 0 occur in adiabatic process, so, dW0 is a perfect differential if the process is adiabatic.
Two events, separated by a (spatial) distance 9 x 109 m, are simultaneous in one inertial frame. The time interval between these two events in a frame moving with a constant speed 0.8 c (where the speed of light c = 3 x 108 m/s) is
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 5
Consider three polarizers P1 ,P2 and P3 placed along an axis as shown in the figure
The pass axis of P1 and P3 are at right angles to each other while the pass axis of P2 makes an angle θ with that of P1 . A beam of unpolarized light of intensity l0 is incident on P1 as shown . The intensity of light emerging from P3 is
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 6
According to malus law the transmitted light intensity is proportional to the square of cosine of angle between polarizer and analyzer.
when light say passing through P1 the angle is q = 0° so
when this polarized light passing through P2 which makes an angle q with P1 and P2 so
Now P1 and P3 are 1 to each other so according to malus law the transmitted intensity
A point particle of mass m carrying an electric charge q is attached to a spring of stiffness constant k. A constant electric field E along the direction of the spring is switched on for a time interval T(whereT Neglecting radiation loss, the amplitude of oscillation after the field is switched off is
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 8
Let, in presence of electric field, the spring elongates by; distance ‘y’
The direction of motion is along y direction, then equation of motion is,
A transistor with β = 100 is used in CE configuration. The collector circuit resistance is 1kΩ& V∞= 20v. Assuming Vbe = 0 find the value of collector to base resistance such that quiescent collector to emitter voltage is 4v
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 9
The phenomenon known as ‘Early effect’ in a bipolar transistor refers to a reduction of the effective-basewidth caused by___
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 10
In a bipolar transistor, the increase in the depletion region of the reverse biased junction, tends to decrease the width of the base with increased reverse voltage. This in turn causes the current gain to increase with increased voltage resulting in a nearly linear increase in current even with the device in the saturation.
A bead of mass m can slide without friction along a massless rod kept at 45° with the vertical as shown in the figure. The rod is rotating about the vertical axis with a constant angular speed ω. At any instant, r is the distance of the bead from the origin. The momentum conjugate to r is
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 11
Identify, the CORRECT energy band diagram for Silicon doped with Arsenic. Here CB, VB, ED and EF are conduction band, valence band, impurity level and Fermi level, respectively.
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 17
As doping with Arsenic Will change the pure silicon Semiconductor into n - type & in n - type SC the free charge carriers are present does to CB because Arsenic is a pentavalent atom thus the atom Thus the fermi Energy level will lie slightly above the middle of the Energy gap & does to ED.
A rod of proper length l0 oriented parallel to the x-axis moves with speed 2c/3 along the x-axis in the. S-frame, where c is the speed of the light in free space. The observer is also moving along the x-axis with speed c/2 with respect to the S-frame. The length of the rod as measured by the observer is
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 19
For finding the length of rod firstly finding the relativistic velocity which is equal to
A system has two energy levels with energies ε and 2ε. The lower is 4-fold degenerate while the upper level is doubly degenerate. If there are N noninteracting classical particles in the system, which is in thermodynamic equilibrium at a temperature T, the fraction of particles in the upper level is
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 21
A mass m is constrained to move on a horizontal frictionless surface. It is set in circular m otion with radius r0 and angular speed w0 by an applied force com municated through an inextensible thread that passes through a hole on the surface as shown in the figure. This force is then suddenly doubled. The magnitude of the radial velocity of the mass
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 26
The particle is moving in a circular motion with radius r0 and angular speed ω0 by an applied force F applied through an inextensible thread passing through hole.
The circular motion of the particle is,
Now. when we doubled the force.
Subtract equation (A) from (B). we get
As the force increases, r will decrease and hence, velocity of particle will decrease till the fall into the hole.
In the voltage regulator shown in the given figure, the load current can vary from 100 mAto 500 mA. Assuming that the Zener diode is ideal (i.e, the Zener knee current is negligibly small and Zener resistance is zero in the breakdown region), the value of R is
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 30
From the circuit given, we have
( Zener knee current is negligibly small)
or- 14Ω < R < 70Ω
Hence, required value of R = 14Ω [closed min value]
A converging lens is used to form an image on screen. When the upper half of the lens is covered by an opaque screen.
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 31
When upper half of the lens is covered image is formed by the rays coming from lower half of the lens. OR image will be formed by the less number of rays. Therefore, intensity of image will decrease. But complete image will be formed.
A beam of light of wavelength 400 nm and power 1.55 mQ is directed at the cathode of a photoelectric cell, (given he = 1240 ev). If only 10% of the current due to these electrons is i . If the wavelength o f light is now reduced to 200 nm, keeping its power the same, the kinetic energy of the electrons is found to increase by a factor of 5. The stopping potentials for the two wavelength are S1 and S2. Then
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 32
Wavelength of incident light λ= 400nm
P = 1.55 mW
Energy of one photon
Number of photons falling per second
Number of electrons ejected is 10% of number of photon falling per second .
N = 0.1 n
Current constipated by flow of ejected electrons
Kinetic theory of ejected electron = Photon - Work function Energy of incident
Where λ = 400nm is reduced to λ = 200nm , the KE increases by 5 times.
In a compton experiment the ultraviolet light of wavelength 2000 A° is scattered from an electron at rest. What should be the minimum resolving power of an optical instrument to measure the compton shift. If the observation is made at 60° and 90° with respect to the direction of the incident light ?
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 33
For uv light of wavelength 2000 A°,
Scallered at an angle θ
Minimum resolving power of instrument required to measure the compton effect
One mole of an ideal gas (r = 1.5) is at pressure of 100 K Pa and a temperature of 300 K. Initial the state of the gas is at the point a of the PV diagram shown. The gas is taken through a reversible cycle a→ b→ c→ a The pressure at point b is 200 K Pa. Then
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 37
Comparing with the process PV-X = constant
During process be, ΔWbc = 0
work done ΔWca = Pdv = 100x103(1m3) = 100KJ
again process ab
A Voltage 200 cos 100 t is applied to a half wave rectifier with load resistance of 5kΩ . Rectifier may be represented by an ideal diode in series with a resistance of 1kΩ
Then which of the following statements is/are correct :-
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 40
An unpolarized lightwave is incident from air on a glass surface at the Brewster angle. Calculate the angle (in degree) between the reflected and the refracted wave.
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 41
Brewster angle is an angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface with no reflection. When unpolarized light is incident at this angle the light that is reflected from the surface is therefore perfectly polarized.
Then the Brewster angle qs
and the angle between Reflected Ray and Refracted Ray will be 90°.
A ball of mass m. initially at rest, is dropped from a height of 5 meters. If the coefficient or restitution is 0.9, the speed of the ball just before it hits the floor the second time is approximately________ m/s (take g = 9.8 m/s2)
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 44
As we know that
The coefficient of restitution =
The velocity at the time of hitting with floor is =
Velocity of approaching =
A particle moves in a plane with velocity such that The time dependence of the magnitude of the velocity = 5t. It is given that r = 1 ,θ =0 and v r > 0 at t = 0. (In the following, you may use e3 ≈ 20.) At what time (in sec.) will θ become 4 radian?
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 47
where c is arbitrary constant which can be evaluated by using initial condition
r = 1 at 9 = θ ⇒ c = 1
Equation of trajectory r(θ)
Magnitude of velocity = 5t
where c is arbitrary constant which can be evaluated using initial condition
A body of mass 1 kg moves under the influence of a central force, with a potential energy function V(r) = Joule, where r is in meters. It is w l found to move in a circular orbit of radius r = 2 m. (In the following, you may use e3 ≈ 20). Find its total energy E. (in mJ)
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 48
Central Force potential energy
Effective potential =
The body moves in a circular orbit of radius r = 2m
So, energy of the system will always be equal to effective potential Ve at r =2m
Also, Ve will be minimum at r = 2m and will be zero at r = 2m
A cylinder of 1 kg mass and 0.02 m diameter left at the top of an inclined plane of height 1 m rolls down without slipping. (Take g = 9.8 ms-2). Find the velocity of center of mass of cylinder on reaching the bottom of inclined plane (in m/sec).
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 49
The kinetic energy of cylinder when it reaches the bottom = potential energy of the cylinder at the top = mgh = 1 x 9.8 x 1 = 9.8 J
Kinetic energy kE = kE of translation + kE of rotation
A parallel beam of light of diameter 1.8 cm contains two wavelengths 4999.75 Å and 5000.25 Å. The light is incident perpendicularly on a large diffraction grating with 5000 lines per centimeter. Using Rayleigh criterion, find the least order at which the two wavelengths are resolved.
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 51
Resolving power required to resolve two wavelengths =
So, Resolving power of grating must be greater than 10000
Resolving power of grating
R = Nn ≥ 10000
So, least order at which two wavelengths are resolved nmin = 2
An aircraft, which weights 12000 kg when unloaded , is on a relief mission , carrying 4000 food packets weighing 1 kg each. The plane is gliding horizontally with its engines off at a uniform speed of 540 kmph when the first food packet is dropped. Assume that the horizontal air drag can be neglected and the aircraft keeps moving horizontally. If one food packet is dropped every second , then the distance between the last two packet drops will be _______ m.
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 54
The mass of an aircraft = 12000 kg
Uniform speed of aircraft is
The distance between the last two packet drops will be equal to the covered distance in one second = 150 m.
In the temperature range 100-1000 C, the molar specific heat of a metal varies with temperature T (measured in degrees Celsius) according to the formula Cp =(1 + T /5 ) J-deg C-1-mol-1. If 0.2 Kg of the metal at 300 C, the final equilibrrium temperature, in degree C, will be ________ .
[Assume that no heat is lost to radiation and /or other effects .]
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 55
m1 = 0.2. T1= 600 C
m2 = 0.1, T2 = 300 C
We know at the thermal equilibrium
Heat absorb = Heat gain
The Zener diode in the regulator circuit shown in the figure has a Zener voltage of 5.8 Volts and a Zener knee current of 0.5 mA. The maximum load current drawn from this circuit ensuring proper functioning over the input voltage range between 20 and 30 volts, is _____ mA.
Detailed Solution for GATE Physics Mock Test Series - 8 - Question 57
Since. VE = 5.8 V always remains constant, therefore maximum load current
when volts (V) is maximum i.e. = 30V
∴ 30 = 1000 x lmax + 5.8
∴ lax = 24.2 mA
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