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Answers posted by priyanka.clay6

2010
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Two cars moving in opposite directions approach each other with speed of $22\; m/s$ and $16.5\; m/s$ respectively. The driver of the first car blows a horn having a frequency $400\; Hz$. The frequency heard by the driver of the second car is [velocity of sound $340\; m/s$] :
answered Feb 15, 2020
By Doppler EffectApparent frequency $n' = n(\large\frac{V+V_o}{V- V_s})$$\qquad \qquad \qquad \qquad...
0 votes
In a common emitter transistor amplifier the audio signal voltage across the collector is $3 \;V$. The resistance of collector is $3\; k \Omega$. If current gain is $100$ and the base resistance is $2 \;k \Omega$, the voltage and power gain of the amplifier is :
answered Feb 15, 2020
$\text{Voltage gain }= \text{current gain } \times \large\frac{R_{output}}{R_{input}}$$A_V = \beta ...
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The ratio of resolving powers of an optical microscope for two wavelengths $\lambda_1 = 4000\; \mathring{A}$ and $\lambda_2 = 6000\;\mathring{A}$ is
answered Feb 15, 2020
Resolving Power $\propto \frac{1}{\lambda}$$\large\frac{RP_1}{RP_2} = \frac{\lambda_2}{\lambda_1} = ...
0 votes
The given electrical network is equivalent to
answered Feb 15, 2020
The given network is $NOR+NOT +NOT = NOR$
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Radioactive material 'A' has decay constant '8 $\lambda$' and material 'B' has decay constant '$\lambda$'. Initially they have same number of nuclei. After what time, the ratio of number of nuclei of material 'B' to that 'A' will be $\frac{1}{e}$ ?
answered Feb 15, 2020
For radioactive decay$N = N_oe^{-\lambda t}$$\large\frac{N_A}{N_B} = \frac{N_o e^{-\lambda t}}{N_o e...
0 votes
Two Polaroids $P_1$ and $P_2$ are placed with their axis perpendicular to each other. Unpolarised light $I_0$ is incident on $P_1$. A third polaroid $P_3$ is kept in between $P_1$ and $P_2 $ such that its axis makes an angle 45º with that of $P_1$. The intensity of transmitted light through $P_2$ is
answered Feb 15, 2020
https://clay6.com/mpaimg/1796_a.jpgBy Malus lawIntensity of light passing through Poloroid $I, P_1 =...
0 votes
A 250 Turn reactangular coil of length 2.1 cm and width 1.25 cm carries a current of $85 \; \mu A$ and subjected to a magnetic field of strength 0.85 T. Work done for rotating the coil by $180^o$ against the torque is :
answered Feb 15, 2020
Work done in rotating the coil through $180^{\circ}$$\qquad W = M \;B\; (\cos 0^{\circ} - \cos 180^{...
0 votes
Consider a drop of rain water having mass $1g$ falling from a height of $1\; km$. It hits the ground with a speed of $50 \;m/s$. Take 'g' constant with a value $10 \;m/s^2$ . The work done by the (i) gravitational force and the (ii) resistive force of air is
answered Feb 15, 2020
Work done by Gravitational force $=mgh$$\qquad \qquad = 1 \times 10^{-3} \times 10 \times 1000 = 10 ...
0 votes
Thermodynamic processes are indicated in the following diagram
answered Feb 15, 2020
Process I - P is Isochoric [ constant volume ]Process II - Q is Adiabatic Process III - R is Isother...
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The angle of incidence for a ray of light at a refracting surface of a prism is $45^o$. The angle of prism is $60^o$. If the ray suffers minimum deviation through the prism, the angle of minimum deviation and refractive index of the material of the prism respectively, are :
answered Feb 15, 2020
https://clay6.com/mpaimg/1795_a.jpg At minimum deviation $r_1 = r_2 = r = A/2$and $\;\;2i = \delta_...
0 votes
A particle of mass 10 g moves along a circle of radius 6.4 cm with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to $8 \times 10^{–4} J$ by the end of the second revolution after the beginning of the motion ?
answered Feb 15, 2020
Kinetic energy $= \frac{1}{2} mv^2 = 8 \times 10^{-4}$$\qquad \qquad \;\; m = 10\;g$$\therefore \fra...
0 votes
A refrigerator works between $4^oC$ and $30^oC$. It is required to remove 600 calories of heat every second in order to keep the temperature of the refrigerated space constant. The power required is : (Take 1 cal = 4.2 Joules)
answered Feb 15, 2020
To keep temperature of refrigerator constant ${\large\frac{Q_1}{W} = \frac{Q_1}{Q_2-Q_1} = \frac{T_1...
0 votes
When an $\alpha$-particle of mass 'm' moving with velocity 'v' bombards on a heavy nucleus of charge 'Ze', its distance of closest approach from the nucleus depends on m as :
answered Feb 15, 2020
When $\alpha $ particles of mass $m$ and velocity bombards a heavy nucleus of charge $(Ze)$ total m...
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An electron of mass m and a photon have same energy E. The ratio of de-Broglie wavelengths associated with them is :
answered Feb 14, 2020
De broglie wavelength of electron$\lambda_e = \large\frac{h}{p} =\frac{h}{\sqrt {2mE}}$De broglie wa...
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An inductor $20 \;mH$, a capacitor $50 \; \mu F$ and a resistor $40\; \Omega$ are connected in series across a source of emf $V = 10 \sin 340t$. The power loss in A.C. circuit is :
answered Feb 14, 2020
Inductive impedence $X_L = 340 \times 20 \times 10^{-3}$$\qquad \qquad \qquad \qquad \qquad = 6.8 \O...
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A uniform rope of length $L$ and mass $m_1$ hangs vertically from a rigid support. A block of mass $m_2$ is attached to the free end of the rope. A transverse pulse of wavelength $\lambda_1$ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is $\lambda_2$. The ratio $\lambda_2/\lambda_1$ is :
answered Feb 14, 2020
Velocity $V = \sqrt{\frac{T}{\mu}}$But velocity $= f \lambda $$\qquad \implies V \propto \lambda \pr...
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A small signal voltage $V(t )= V_0 \sin \omega t$ is applied across an ideal capacitor C :
answered Feb 14, 2020
For an ideal capacitor, current $I$ leads the voltage by $90^{\circ}$ and capacitor does not consume...
0 votes
What is the minimum velocity with which a body of mass m must enter a vertical loop of radius R so that it can complete the loop ?
answered Feb 14, 2020
When a body makes a vertical loops at the top most point it must be having minimum velocity $= \sqr...
0 votes
A uniform circular disc of radius 50 cm at rest is free to turn about an axis which is perpendicular to its plane and passes through its centre. It is subjected to a torque which produces a constant angular acceleration of $2.0\; rad\; s^{–2}$ . Its net acceleration in $ms^{–2}$ at the end of 2.0 s is approximately :
answered Feb 14, 2020
Angular acceleration $\alpha = 2 \;rad/s^2$ Radius $R = 0.5 \;m$ Time $t = 2\;sec$ ...
0 votes
A piece of ice falls from a height h so that it melts completely. Only one-quarter of the heat produced is absorbed by the ice and all energy of ice gets converted into heat during its fall. The value of h is : [Latent heat of ice is $3.4 \times 10^5 \;J/kg$ and $g = 10\; N/kg$]
answered Feb 14, 2020
Heat used up for melting = $\frac{1}{4}$ (Potential energy loss)$mL_f = \frac{1}{4} mgh$$\qquad h =...
0 votes
A particle moves so that its position vector is given by $\overrightarrow{r} = \cos \omega t \;\hat{x} + \sin \omega t \;\hat{y}$. Where $\omega$ is a constant.
Which of the following is true ?
answered Feb 14, 2020
Position vector of particle$\overrightarrow{r} = (\cos wt) \hat{i} +(\sin w t) \hat{j}$$\overrightar...
0 votes
Two identical charged spheres suspended from a common point by two massless strings of length l, are initially at a distance $d\; (d << l)$ apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity v. Then v varies as a function of the distance x between the spheres, as :
answered Feb 14, 2020
https://clay6.com/mpaimg/1793_a.jpgAt balance $T \sin \theta =\large \frac{Kq^2}{d^2}$and $T \cos \t...
0 votes
A disk and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first ?
answered Feb 12, 2020
Since the incline has same height and length the angle is same.The acceleration of the two objects w...
0 votes
If the velocity of a particle is v =$At + Bt^2$, where $A$ and $B$ are constants, then the distance travelled by it between 1s and 2s is :
answered Feb 12, 2020
Velocity $V =At + Bt^2$ Displacement $=\displaystyle\int V \;dt$$\qquad \qquad \qquad =\displaystyle...
0 votes
Match the corresponding entries of column 1 with column 2. [Where m is the magnification produced by the mirror] :
answered Feb 12, 2020
Magnification $m=-2 \implies \text{concave mirror and real image}$$m = -1/2 \implies \text{concave ...
0 votes
A long straight wire of radius a carries a steady current $I$. The current uniformly distributed over its cross-section. The ratio of the magnetic fields $B$ and $B'$, at radial distance $\frac{a}{2}$ and $2a$ respectively, from the axis of the wire is :
answered Feb 12, 2020
https://clay6.com/mpaimg/1790_a.jpg$B_{inside} = \large\frac{\mu_o I a/2}{2 \pi a^2} = \frac{\mu_o I...
0 votes
A gas is compressed isothermally to half its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to half. Then :
answered Feb 12, 2020
Isothermal change $V_1 = V ; \qquad V_2 = V/2$$\therefore P_1V_1 = P_2V_2\qquad \implies P_1V=P_2V/...
0 votes
A npn transistor is connected to common emitter configuration in a given amplifier. A load resistance of $800 \Omega$ is connected in the collector circuit and the voltage drop across it is $0.8\; V$. If the current amplification factor is $0.96$ and the input resistance of the circuit is $192 \Omega$, the voltage gain and the power gain of the amplifier will respectively be :
answered Feb 12, 2020
Current amplification factor $\beta = 0.96$$R_L = 800 \; \Omega; \;\; V_o = 0.8 \;V$$R_I = 192 \Omeg...
0 votes
An astronomical telescope has objective and eyepiece of focal lengths 40 cm and 4 cm respectively. To view an object 200 cm away from the objective, the lenses must be separated by a distance :
answered Feb 12, 2020
Focal length of objective $= f_o=40\;cm$Focal length of eye piece $= f_e= 4 \;cm$ https://clay6.com/...
0 votes
If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is :
answered Feb 12, 2020
Magnitude of sum of two vectors = magnitude of difference $|\overrightarrow{A}+\overrightarrow{B} |=...
0 votes
Consider the junction diode as ideal. The value of current flowing through AB is :
answered Feb 12, 2020
https://clay6.com/mpaimg/1786_a.jpgDiode is in forward bias$I = \large\frac{P.D.}{Resistance }$$\;\;...
0 votes
The molecules of a given mass of a gas have r.m.s velocity of $200 \; ms^{-1}$ at $27^oC$ and $1.0 \times 10^5 \; Nm^{-2}$ pressure. When the temperature and pressure of the gas are respectively, $127^oC$ and $ 0.05 \times 10^5 \; Nm^{-2}$, the r.m.s. velocity of its molecules in $ms^{-1}$ is :
answered Feb 12, 2020
$Rms\; velocity \;V_{rms} \propto \sqrt{T}$$\large\frac{V_2}{V_1} = \sqrt{\frac{T_2}{T_1}}$$\qquad =...
0 votes
An air column, closed at one end and open at the other, resonates with a tuning fork when the smallest length of the column is 50 cm. The next larger length of the column resonating with the same tuning fork is :
answered Feb 12, 2020
For air column closed at one end, the resonance length is $\ell_1$The next resonating length will be...
0 votes
A black body is at a temperature of $5760 \;K$. The energy of radiation emitted by the body at wavelength $250 \;nm$ is $U_1$, at wavelength $500 \;nm$ is $U_2$ and that at $1000\; nm$ is $U_3$. Wien's constant, $b = 2.88 \times 10^6 \;nmK$.
Which of the following is correct ?
answered Feb 12, 2020
By Wein's displacement law,$\qquad \lambda_m \times T = b$where $\lambda_m$ is having maximum energy...
0 votes
A square loop ABCD carrying a current i is placed near and coplanar with a long straight conductor XY carrying a current I, the net force on the loop will be :
answered Feb 12, 2020
https://clay6.com/mpaimg/1785_a.jpgForce on AB is attraction $= \large\frac{\mu_oI i}{2 \pi (L/2)}$F...
0 votes
In a diffraction pattern due to a single slit of width 'a', the first minimum is observed at an angle $30^o$ when light of wavelength $5000\; Å$ is incident on the slit. The first secondary maximum is observed at an angle of
answered Feb 12, 2020
Diffraction pattern due to single slit, for first minima$\qquad \sin \theta = \frac{\lambda}{a} \qqu...
0 votes
From a disc of radius R and mass M, a circular hole of diameter R, whose rim passes through the centre is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis, passing through the centre ?
answered Feb 12, 2020
https://clay6.com/mpaimg/1784_a.jpgMass of the removed part = Mass per unit area $\times $ Area of h...
0 votes
Two non-mixing liquids of densities $\rho$ and $n \rho \;(n > 1)$ are put in a container. The height of each liquid is $h$. A solid cylinder of length $L$ and density $d$ is put in this container. The cylinder floats with its axis vertical and length pL $(p < 1)$ in the denser liquid. The density $d$ is equal to :
answered Feb 12, 2020
https://clay6.com/mpaimg/1783_a.jpgVolume of liquid of density $n \rho$ displaced $= (p L A)$upthrus...
0 votes
A body of mass $ 1 \;kg$ begins to move under the action of a time dependent force $\overrightarrow{F} = (2 t \hat{i} + 3 t^2 \hat{j}) N$, where $\hat{i}$ and $\hat{j}$ are unit vectors along x and y axis. What power will be developed by the force at the time $t$ ?
answered Feb 12, 2020
$Force = mass \times acceleration$$\overrightarrow{F} = m \overrightarrow{a}$$\overrightarrow{a} = \...
0 votes
A siren emitting a sound of frequency $800\; Hz$ moves away from an observer towards a cliff at a speed of $15ms^{–1}$. Then, the frequency of sound that the observer hears in the echo reflected from the cliff is : (Take velocity of sound in air = $330 \; ms^{-1}$
answered Feb 12, 2020
Source is moving cliff with velocity $V_s$ and gets reflected back to the observer.$\therefore $ App...
0 votes
The magnetic susceptibility is negative for :
answered Feb 12, 2020
Magnetic susceptibility is negative for diamagnetic material only.
0 votes
A car is negotiating a curved road of radius $R$. The road is banked at an angle $\theta$. The coefficient of friction between the tyres of the car and the road is $\mu_s$ . The maximum safe velocity on this road is :
answered Feb 12, 2020
https://clay6.com/mpaimg/1781_a.jpg Necessary centripital force is provided by $(N \sin \theta + \m...
0 votes
A long solenoid has $1000\; turns$. When a current of $4A$ flows through it, the magnetic flux linked with each turn of the solenoid is $4 \times 10^{–3}\; Wb$. The self-inductance of the solenoid is :
answered Feb 12, 2020
Number of turns in solenoid $N = 1000$Current $I = 4A$$\phi$ Magnetic flux $= 4 \times 10^{-3} Wb$$\...
0 votes
The ratio of escape velocity at earth $(v_e)$ to the escape velocity at a planet $(v_p)$ whose radius and mean density are twice as that of earth is :
answered Feb 12, 2020
Escape velocity $V_{esc} = \sqrt{\frac{2GM}{R}}$$\qquad \qquad \qquad = \sqrt{2.G. \frac{4 \pi R^3 \...
0 votes
Given the value of Rydberg constant is $10^7 \;m^{-1}$, the wave number of the last line of the Balmer series in hydrogen spectrum will be :
answered Feb 11, 2020
Rydberg constant $R = 10^7 m^{-1}$Wave number $= \frac{1}{\lambda} $$\qquad \qquad = RZ^2[\frac{1}{...
0 votes
The intensity at the maximum in a Young’s double slit experiment is $I_0$. Distance between two slits is $d = 5 \lambda$, where $\lambda$ is the wavelength of light used in the experiment. What will be the intensity in front of one of the slits on the screen placed at a distance $D = 10 \;d$ ?
answered Feb 11, 2020
https://clay6.com/mpaimg/1780_a.jpg$S_1P =10d =10(5 \lambda) =50 \lambda$Path difference $S_2P-S_1P ...
0 votes
Coefficient of linear expansion of brass and steel rods are $\alpha_1$ and $\alpha_2$. Lengths of brass and steel rods are $l_1$ and $l_2$ respectively. If $(l_2 – l_1)$ is maintained same at all temperatures, which one of the following relations holds good ?
answered Feb 11, 2020
$\Delta L_{Brass} = \ell_1(1+\alpha_1 \Delta T)$$\Delta L_{Steel} = \ell_2(1+\alpha_2 \Delta T)$$\De...
0 votes
At what height from the surface of earth the gravitation potential and the value of $g$ are $– 5.4 \times 10^7 \;J \;kg^{–2}$ and $6.0\; ms^{–2}$ respectively ? Take the radius of earth as $6400\; km$ :
answered Feb 11, 2020
Gravitational potential at height $h = -5.4 \times 10^7\; J/kg^2$$\qquad V = \large\frac{GM}{R+h} = ...
0 votes
The charge flowing through a resistance $R$ varies with time $t$ as $Q = at – bt^2$ , where $a$ and $b$ are positive constants, The total heat produced in R is :
answered Feb 11, 2020
Charge $Q =at -bt^2$Current $I = \large\frac{dQ}{dt} = a-2bt$at $I = 0$$\implies t = \large\frac{a}{...
0 votes
Out of the following options which one can be used to produce a propagating electromagnetic wave ?
answered Feb 11, 2020
When charge is accelerated it produces electromagnetic waves.
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