A wooden block P is at rest on the horizontal surface of a wooden platform M. The coefficient to static friction between these two is μ. The platform starts moving suddenly with a uniform acceleration "a". The minimum value of "a" so that the block P starts moving with respect to the platform M is (g denotes the acceleration due to gravity).
A block of mass 2 kg is initially held at rest on the frictionless surface of a wedge of mass 6 kg. The wedge itself lies on horizontal frictionless surface. The block is now released so that it is allowed to slide down the slope. How far down the slope does the block move when the wedge has moved a distance of 2 cm?
A particle of mass m moves along the x-axis under the influence of the potential V(x) = V0αx2. If the particle oscillate with a small amplitude around the minimum of the potential, what is the period of oscillation? Take m = 4, V0 = 2 and α 3/4.
Two beakers A and B are filled to the brim with water at40C. beaker A is cooled 'while beaker B is heated. This is likely to result in
We know that the density of water is maximum at 40C and hence the volume is minimum at 40C. On heating or cooling (in both the cases) the volume of water will increase. Hence the water will overflow in both beakers.
A galaxy is receding relative to us at a speed of 3000 km/sec. It emits hydrogen red line of wavelength 6500 A0. When seen by us the wave length of this radiation will appear to be
In o rd e r to determine the age of ancient wooden tools, radio carbon dating method is used. This is done by measuring the fraction of radioactive isotope 14C of carbon compared to the normal (non-radioactive) isotope 12C in a sample.
An old sample is found to contain 1/5 times the fraction of 14C as compared to a fresh piece of wood. Given that the half-life of 14C is 5500 yr, the approximate age of the old sample is
Consider a pipe of length 80 cm with both ends open. How many modes of oscillations of the air column are possible upto a frequency of 1450 Hz? (Take the speed of sound to be 330 m/sec.)
A young's double slit apparatus has a slit separation of 0.4 mm and a screen placed at a distance of 200 cm from the slits. When illuminated by a 632 nm Helium Neon laser, the position of the first intensity minimum with respect to the central maximum will be
A small block of copper with a specific heat of 200 cal/0C is initially at a temperature of 3000C. It is then dropped into a large tank of water maintained at 270C. What is the change in entropy of the combined system after equilibrium is established?
A solid is melts into a liquid via first-order phase transition. The relationship between the pressure P and the temperature T of the phase transition is P = where P0 is a constant. The entropy change associated with the phase transition is 3J mole-1 k-1. The clausius - clapeyron equation for the latent heat is is the change in molar volume at the phase transition. Then
We know clausius-clapeyron equation.
Consider the matrix
the eigenvalues of A are, (i = √-1)
Sum of eigenvalues = trace of matrix = 0
Product of eigenvalues = Det. of matrix = -1
Only option (D) is possible answer.
Which of the following graphs correctly represent the variation of with P for an ideal gas at constant temperature?
Compressibility of gas
A horizontally placed hollow tube has a cross-sectional area A at the beginning of the tube that gradually tapers off to A/2 at the end. An incompressible, ideal fluid of density ρ enters the tube with a velocity V at the beginning of the tube. The difference in the pressure across the tube is
According to equation of continuity velocity at the other end V = 2V
Applying ρ Bernoulli equation
A satellite is placed in a circular orbit about the earth whose radius is 1/50 th the distance between the earth and the moon. If the lunar period around the earth is 28 days, the period of revolution of the satellite is approximately.
According to Kepler's third law
Planck's constant (h), the speed of light in vacuum (C), Length (L) and Newton's gravitational constant (G) are four fundamental constants of nature. Which of the following combinations has the dimension of frequency?
A stone is dropped from a height 200 m at the equator. The eastward deflection is
The deflection is given by the formula
where θ is the latitude at the equator θ = 0
A block of mass m slides on a frictionless table. It is constrained to move inside a ring of radius R. At time t = 0 , block is moving along the inside of the ring (i.e. in the tangential direction) with velocity v0 The coefficient of friction between the block and the ring is μ . Find the speed of the block at time t
N = mv2/R
fmax = μN = μmv2/R
:. Retardation a = fmax/m
:. (−dv/dt) = μv2/R
or ∫(v0 to v)dv/v2 = −μ/R∫(0 to t)dt
or v = v0/(1 + μv0t/R)
A particle of charge +q and mass m moving under the influence of a uniform electric field and a uniform magnetic field follows a trajectory from P to Q as shown in the figure. The velocities at P and Q are Which of the following statement is not correct?
Work done by the electric force = Change of kinetic energy
A bullet of mass m moving horizontally with speed V passes through a pendulum suspended using a string of length t and bob of mass M and emerges with velocity V/3. The minimum velocity of V which makes the pendulum to swing through a complete circle is
The speed of the bob immediately after the bullet passes through it is given by the law of momentum conseivation
We know that the minimum velocity, Vmin at the lowest position so that it completes a circle is
A cylindrical vessel of height h and base are A is filled with water. An orifice of area a « A is opened in the bottom of the vessel, determine how soon all the water will pour out of the vessel.
Water jet coming out from the orifice of area a at an arbitrary instant of time when the height of water column in the cylindrical vessel is H.
As the rate of out-flux should be equal to the rate with which volume of the water in the vessel decreases
The orthorhombic crystal has axial units in the ratio of 0.424 : 1: 0.367. The miller indices of a crystal face whose intercepts are in the ratio 0.212 :1 :0.183 will be : -
a : b : c :: 0.424 :1 : 0.367
p x 0.424 = 0.212
Similarly bq = 1
q x 1
∴ q= 1
& rc = 0.183
Two isolated metallic solid sphere of radius R & 2R are charged such that both of these have same charge density σ. The sphere are located for away from each other if they are connected by a thin conducting wire. The charge density on the bigger sphere:-
As 'σ' on both the sphere is same ;
Now, during sharing charge is distributed in proportion to capacity i.e. radius so charge on the bigger sphere
If a conductor of cross section 'a' & carrying a current is oriented along the y-axis in a magnetic field the force density exerted on the conductor is :-
The time averaged poynting vector in for a wave with in free space:-
In a multistage RC coupled amplifier the coupling capacitor (Cc):-
Coupling capacitance comes in series with the circuit and hence affects low frequency response as at low frequency its impedance becomes high. It also blocks dc but affect the frequency response.
In a transistor having fixed biasing, the forward bias across the base-emitter junction is kept constant & the reverse bias across the collector-base junction is increased. Neglecting the leakage current across the collector-base junction & the depletion region generation current, the base current will : -
The base current will increase on increasing the reverse biasing of CB junction.
Thermal runway in a transistor biased in the active region is due to : -
Thermal runway in a transistor biased in the active region is due to change in reverse collector saturation current due to rise in temperature .
A voltage source VAB = 4 sin ωt is applied to the terminals A & B of the circuit shown in the given figure. The diodes are assumed to be ideal. The impedance by the circuit across the terminals A & B is:-
Diode D1 conducts through 10 kΩ on the extreme right & Diode D2 conduct through the 10 kΩ in the middle branch Diode D1 is blocked.
Then the source always sees a resistance of 10kΩ..
Given that the op-amp configuration in given figure below, the value of R( required to produce a closed loop voltage gain of 100:-
Eigen vector of matrix corresponding to the eigen values (1 + i) and (1 - i) are respectively (where i = √-1)
Identify the incorrect statement for the vectors
Which of the following are correct. If an object of mass m rests on a surface with coefficient of static friction μ.
Which of the following statements concerning the Compton effect are correct?
Since, for compton effect
Hence, the photon transfers maximum energy to the electron.
Which of the following are first order phase transition?
Vaporization of a liquid (liquid to gas) at its boiling point in which only phase is changed, is the first order phase transition but in other two options, the structure of material is changed, so these are second order phase transition.
Which of the following relations are correct?
Using Maxwell relation
Using Maxwell's relation
A particle of energy E is incident from the left on a potential step of height V 00 at x = 0. Select the correct statements.
Consider two conducting plates of infinite extent, one plate at z = 0 & the other at Z = L, both parallel to the xy plane. The vector potential & scaler potential in the region between plates is given by:-
For this to represent a standing wave in the empty region between the plates (k)
A monochromatic light of λ = 5000 A0 is incident on two slit separated by a distance of 5 x 10-4m. The interference pattern is seen on a screen placed at a distance of 1m from the slits. A thin glass plate of thickness 1.5 x10-6 m and refractive index μ = 1.5 is placed between one of the slits & the screen.
Shifting of central maximum by the introduction of a thin glass plate is lateral shift of the central maximum is given by :-
Consider the self biased circuit given in the figure. If driven by a current source choose the correct statement :-
Only option A is correct since lB is constant .self bias is not operative.
In the figure shown alternative position & negative charge of magnitude q are placed at the current of a cube of side length 'a'.
Initial electrostatic potential energy of the system:-
are two quantum mechanical operators. If stands for the commutator of then is equal to ________ .
The normalized wave functions ψ1 and ψ2 correspond to the ground state and the first excited state of a particle in a potential. Given the information that the operator Â acts on the wave function as
The expectation value of A for the state is ________.
The rate of clock in a spaceship 'Aakshganga* is observed from earth to be 5/13 of the rate of the clock on earth. If both Suryashakti and Aakshganga are moving in same direction relative to someone on earth, then the speed of Aakashganga relative to suryashakti is nc. The value of n is ______ .
(Given : The velocity of Suryashakti is 4/5 c with respect to Earth)
A particle of mass 1 kg is attached to a thin uniform rod of length 1 m and mass 4 kg. The distance of the particle from the centre of mass of the rod is 1/4 m.
The moment of inertia of the combination about an axis passing through 0 normal to the rod is _________ .
A spring mass system has undamped natural angular frequency ω0 = 50 rad s-1. The solution x(t) at critical damping is given by where x0 is a constant, at whattime (sec) the system experiences the maximum damping force.
The activity of a radioactive sample is decreased by 75% of the initial value after 60 days. The half life (in days) of the sample is approximately is ____.
A car tyre is slowly pumped up to a pressure of 2 atm in an environment at 150C. At this point, it bursts. Assuming the sudden expansion of the air (a mixture of O2 and N2) that was inside the tyre to be adiabatic, its temperature (in K) after the burst is ______.
A tiny particle of mass 1.38 x 10-11 kg is floating in air at 3000C. Ignoring gravity, its rms speed (in μm/sec) due to random collisions with air molecules will be closest to ______.
If S is the closed surface enclosing a volume 1m3 and is the unit normal vector to the surface is position vector, then the value of the following integral is ______.
According to Gauss's theorem the surface integral of the normal component of a vector function F tapes around a closed surface S is equal to the integral of the divergence of F taken over the volume C(1m3) enclosed by surface.
A plane harmonic wave travelling through a medium is represented by
The refractive index of the medium at this frequency will be _______.
The wave function for a particle constrained to move in one dimensional is shown in the graph above The probability that the particle would be found between x = 2 and x = 4 is _____.
A light damped harmonic oscillator loses energy at the rate of 4% per minute. The decrease in amplitude of the oscillator per minute will be cosest to _____.
An x-ray beam of wavelength 0.97A0 is obtained in the third-order after reflection at 600 from the crystal plane. Another beam is obtained in the first order after reflection at 300 from the same crystal calculate the wavelength of the two-second x-ray beam (in A0)?
Calculate the lattice constant for a rock salt crystal (density equal to 2.18 gm/cm3). Given that the crystal has fcc lattice & molecular weight of 58.5 gm (in A0)?
What is the minimum number of NAND gates required to implement y =
The gain of the amplifier shown in figure, if the open loop voltage gain of the op-amp is 100,00?
This is an non-inverting operational ampifier configuration
In a homogeneous, non-conducting region where μr = 1, the value of εr will be [Given :-
A railway engine passes by the platform at a speed of 36 km/h blowing its whistle having a frequency of 660 Hz. Calculate the difference in the frequencies of the whistle heard by a person standing on the platform as the engine goes past the person.
According to Doppler effect when source moves toward observer. The frequency increases, hence apparent frequency is given as
A diffraction grating of length 3.5 x 10-2 m is illuminated by a light of wavelength 4997A0 & 5003A0. The maximum size of the grating element d (in μm) required to resolve the two wavelength in the first order _____:-
A Michelson interferometer is illuminated with monochromatic light. When one of the mirror is moved through a distance of 20.3μm, 82 fringes pass through the cross-wire. The wavelength of the monochromatic light is _______(in nm).
In Michelson interferometer; the path differential must satisfy the condition of maxima; Let initially the no. of fringe is 'n', then