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A narrow slit S transmitting light of wavelength $\lambda$ is placed a distance d above a large plane mirror as shown in figure (17-E1). The light coming directly from the slit

and that coming after the reflection interfere at a screen $\sum$ placed at a distance D from the slit. (a) What will be the intensity at a point just above the mirror, i.e., just above O? (b) At what distance from O does the first maximum occur?

The displacement of the particle at x = 0 of a stretched string carrying a wave in the positive x-direction is given by f(t) =A sin(t/T). The wave speed is v. Write the wave equation.

Two metallic spheres $S_1$ and $S_2$ are made of the same material and have identical surface finish. The mass of $S_1$ is three times that of $S_2$. Both the spheres are heated to the same high temperature and placed in the same room having lower temperature but are thermally insulated from each other. The ratio of the initial rate of cooling of $S_1$ to that of $S_2$ is

Construct Index of Industrial Production (IIP) from the following data:

A sonometer wire resonates with a given tuning fork, forming standing waves with five antinodes between the two bridges when a mass of $9\text{kg}$ is suspended from the wire. When a mass of $M\text{kg}$ is suspended from the wire, the same tuning fork causes the wire to form three antinodes for the same positions of the bridges. What is the value of $M$?

A circular coil of radius 2.00 cm has 50 turns. A uniform magnetic field B = 0.200 T exists in the space in a direction parallel to the axis of the loop. The coil is now roated about a diameter through an angle of ${60.0}^{\circ }$. The operation takes 0.100 s.

(a) Find the average emf induced in the coil.

(b) If the coil is a closed one (with the two ends joined together) and has a resistance of 4.00 $\Omega$, Calculate thene3t charge crossing a cross-section of the wire of the coil.

Figure shows a circular coil of N turns and radius a, connected to a battery of emf $\epsilon$ through a rheostat. The rheostat has a total length L and resistance R. The resistance of the coil is r. A smalll circular loop of radius a' and resistance r' is placed coaxially with the coil. The centre of the loop is at a distance x from the centre of the coil. In the beginning, the sliding contact of the rheostat is at the left end and then sliding contact of the rheosts is at the left end and then onwards it is moved towards right at a cinstant speed v. Find the emf induced in the small circular loop at the instant

(a) The contact begins to slide and

(b) It has slid through hals the length of the rheostat.

Water rises in a capillary tube to a certain height such that the upward force due to surface tension is balanced by $75\times {10}^{-4}\text{N}$ force due to the weight of the liquid. If the surface tension of water is $6\times {10}^{-2}{\text{Nm}}^{-1}$, the inner circumference of the capillary must be

de Broglie’s wavelength is related to applied voltage using the equation.

Pressure exerted by saturated water vapour is called aqueous tension. What correction term will you apply to the total pressure to obtain pressure of dry gas?

A metallic rod of length I is tied to a non-conducting string of length 2l and made to rotate with angular speed $\omega$ on a horizontal table with one end of the string fixed. If there is a vertical magnetic field B in the region, the emf induced across the ends of the rod is

A wheel is rotating about a fixed axis through its center 300 rpm. A constant torque starts acting on it, opposing its motion. Before coming to rest it makes 25 complete rotations. If the moment of inertia of the wheel about the axis of rotation is $⟮\frac{10}{\pi }⟯kg{m}^2$, the torque (in N-m) acting on it is

A thin wire of variable mass per unit length $\mu ={\mu }_{0}x$, is hanging from the ceiling as shown in the figure the length of wire is $L_0$. A small transverse disturbance is produced at its lower end. Find the time after which the disturbance will reach to the other ends?
(x is calculated from lower end)

A proton and an alpha particle both enter a region of uniform magnetic field $B$, moving at right angles to the field $B$. If the radius of circular orbits for both the particles is equal and the kinetic energy of the proton is $1MeV$, the energy of the alpha particle will be

A pressure cooker of volume $10$ litres contains an ideal gas at atmospheric pressure ${10}^5$ Pa and temperature of $27°C$. It has a whistle which has an area of $0.1c{m}^2$ and mass of $100gm$. To what temperature should it be heated so that the whistle is just lifted up?

The power factor of the circuit shown below is $1/\sqrt{2}.$ The capacitance of the circuit is equal to

Thermal coefficient of volume expansion at constant pressure for an ideal gas sample of $n$ moles having pressure $P_o$, volume $V_o$ and temperature $T_o$ is:

The point S is monochromatic source of light emitting light of wavelength $\lambda .$ At the point P at a distance x from the mirror as shown in the figure, interference takes place between two light rays one directly coming from source S and another after reflection from the mirror such that a maxima is formed. The value of x may be:

Choose the correct relations on the basis of Bohr’s theory:

A capacitor of capacitance C is charged fully using a battery of e.m.f, E . It is then
disconnected form the battery . If the separation between the plates of the capacitor is
now doubled. What will happen to : Charge stored by the capacitor,P.D across it, field
strength between the plates and energy stored between the plates of the capacitor.. Answer the question again, if the battery is kept connected

A body cools down from ${40}^{\circ }\text{C}$ to ${35}^{\circ }\text{C}$ in $10$ minutes and to ${30}^{\circ }\text{C}$ in another $15$ minutes. Find the temperature of the surroundings.

Why is it difficult to walk on a slippery road?

The graph shown below represents the variation of the force as a function of position for a body.


Find out the work done by the force in moving the body from $x=3\text{m}$ to $x=7\text{m}$.

Figure shows a spring fixed at the bottom end of an incline of inclination ${37}^{\circ }$. A small block of mass $2\text{kg}$ starts slipping down the incline from a point $5.8\text{m}$ away from the spring. The block compresses the spring by $20\text{cm}$, stops momentarily and then rebounds through a distance of $1\text{m}$ up the incline. The friction coefficient between the plane and the block and the spring constant of the spring is (Take $g=10{\text{m/s}}^2$)

Column I gives physical quantities based on a situation in which an ideal cell of emf $V$ is connected across a cylindrical rod of uniform cross-section area and conductivity $\left(\sigma \right)$ as shown in figure. $E,J,\varphi$ and $i$ are electric field at, current density through, electric flux through and current through shaded cross-section respectively as shown in figure. Match the expression in Column I with the statements in Column II.

$\begin{array}{cccc}& \text{Column -I}& & \text{Column-II}\\ \text{(A)}& \frac{\varphi }{i}& \text{(P)}& \text{Conductivity of rod}\\ \text{(B)}& \frac{E}{J}& \text{(Q)}& \text{Resistance of rod}\\ \text{(C)}& \sigma \varphi V& \text{(R)}& \text{Resistivity of rod}\\ \text{(D)}& \frac{V}{\sigma phi}& \text{(S)}& \text{Power delivered to rod}\end{array}$
Which of the following is the only CORRECT combination ?

A force $F$ is applied to a block of mass $2\sqrt{3}\text{kg}$ as shown in the diagram. What should be the maximum value of force so that the block does not move?

Two equal charges are suspended with non-conducting wires of equal length from the same point. Now, the whole system is taken inside a liquid (water). If the angle between the threads remains same, then calculate the relative permittivity of water. Relative density of both charged particles is $\sigma$.

A man of mass M stands on a weighing machine in an elevator accelerating upwards with an acceleration $a_0$ . Calculate the reading of the weighing machine

The speed of a wave in a certain medium is 960 m/s. If 3600 waves pass over a certain point of the medium in 1 min, the wavelength is

A boy is standing on a platform which is free to rotate about its axis. The boy holds an open umbrella in his hand. The axis of the umbrella coincides with that of the platform. The moment of inertia of "the platform plus the boy system" is 3.0 $\times {10}^{-3}{\text{kg-m}}^2$ and that of the umbrella is 2.0 $\times {10}^{-3}{\text{kg-m}}^2$. The boy starts spinning the umbrella about the axis at an angular speed of 2.0 rev/s with respect to himself. Find the angular velocity imparted to the platform

In an a.c. circuit, the instantaneous e.m.f. and current are given by
$e=100\sin 30t$
$i=20\sin (30t-\frac{\pi }{4})$
In one cycle of a.c., the average power consumed by the circuit (in watts) and the wattless current (in amperes) are respectively (Assume SI units)

Water is flowing through a long horizontal tube. Let P_A and P_B be the pressures at two points A and B of the tube.

An open tank with a square base and vertical sides is to be constructed from a metal sheet so as to hold a given quantity of water. Show that the cost of material will be least when depth of the tank is half of its width. If the cost is to be borne by nearby settled lower income families, for whom water will be provided. what kind of value is hidden in this question ?

The amplitude and the time period in a S.H.M. is 0.5 cm and 0.4 sec respectively. If the initial phase is $\frac{\pi }{2}$ radian, then the equation of S.H.M. will be

If tan$\alpha$ = $\frac{m}{m+1}$ and tan$\beta$ = $\frac{1}{2m+1}$, then $\alpha$ + $\beta$ =

[IIT 1978; EAMCET 1992; Roorkee 1998; JMI EEE 2001]

In the figure, $m_A=2\text{kg}$ and $m_B=4\text{kg}$. The minimum value of $F$ for which $A$ starts slipping over $B$ is $(g=10{\text{ms}}^{-2})$

The angular velocity of the revolution of a planet around the sun increases because

The average kinetic energy of translation of a molecule of an ideal gas at temperature T is:

A $\text{SHM}$ is represented by the equation $x=10\text{sin}(\pi t+\frac{\pi }{6})$ in SI units. Find the maximum velocity of particle executing $\text{SHM}$.

The angular momentum of a body is 31.4 Js and its rate of revolution is 10 cycle per second. The momentum of inertia of the body about the axis of rotation is