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(i) A point object is placed in front of a double convex lens (or refractive index `mu=n_2/n_1` with respect to air) with its spherical faces of radii of curvature `R_1 and R_2` Show the path of rays due to refraction at first and subsequently at the second surface to obtain the formation of the real image of the object. Hence, obtain the lens maker's formula for a thin lens. (ii) A double convex lens having both faces of the same radius of curvature has refractive index 1.55. Find out the radius of curvature of the lens required to get the
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A cylinder with a movable piston contains 3 moles of hydrogen at standard temperature and pressure. The walls of the cylinder are made of a heat insulator, and the piston is insulated by having a pile of sand on it. By what factor does the pressure of the gas increase if the gas is compressed to half its original volume
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Match the Column I (electric lines of force) with Column II (types of charge) and select the correct answer from the codes given below. Column I Column II A. p.A pair of equal and opposite charges B. q. A pair of positive charges C. r. A single positive charge D. s. A single negative charge
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The electric field components in Fig. are Ex = αx 1/2 , Ey = Ez = 0, in which α = 800 N/C m1/2. Calculate the flux through the
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Three vessels of equal capacity have gases at the same temperature and pressure. The first vessel contains neon (monatomic), the second contains chlorine (diatomic), and the third contains uranium hexafluoride (polyatomic). Do the vessels contain equal number of respective molecules ? Is the root mean square speed of molecules the same in the three cases? If not, in which case is vrms the largest
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Consider three charges q1 , q2 , q3 each equal to q at the vertices of an equilateral triangle of side l. What is the force on a charge Q (with the same sign as q) placed at the centroid of the triangle, as shown
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Assertion: Away from a charge field lines gets weaker and density of field lines is less, resulting in well separated lines. Reason Only a finite number of lines can be drawn from a
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Two point charges of +16µc and –9µc are placed 8 cm apart in air. ............... distance ofa point from –9µc charge at which the resultant electric field is
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Faraday Cage A Faraday cage or Faraday shield is an enclosure made of a conducting material. The fields within a conductor cancel out with any external fields, so the electric field within the enclosure is zero.These Faraday cages act as big hollow conductors. You can put things to shield them from electrical fields. Any electrical shocks the cage receives, pass harmlessly around the outside of the cage. Which of the following material can be used to make a Faraday
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When the charge of a body becomes half, the electric field
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Two small similar metal spheres A and B having charges 4q and – 4q, when placed at a certain distance apart, exert an electric force F on each other. When another identical uncharged sphere C, first touched with Athen with B and then removed to infinity, the force of interaction between A and B for the same separation will
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For an LCR series circuit, phasors of current i and applied voltage `V=V_0 sinomegat` are shown in diagram at `t =0`. Which of the following is/are
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chapter7
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The motion of a particle executing simple harmonic motion is described by the displacement function, x(t) = A cos (ωt + φ ). If the initial (t = 0) position of the particle is 1 cm and its initial velocity is ω cm/s, what are its amplitude and initial phase angle ? The angular frequency of the particle is π `s^(–1)`. If instead of the cosine function, we choose the sine function to describe the SHM : x = B sin (ωt + α), what are the amplitude and initial phase of the particle with the above initial
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Consider a metal ring kept (supported by a cardboard) on top of a fixed solenoid carrying a current I (see Fig ). The centre of the ring coincides with the axis of the solenoid. If the current in the solenoid is switched off, what will happen to the
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A condenser of capacity `6 µF` is fully charged using a 6-volt battery. The battery is removed and a resistanceless 0.2 mH inductor is connected across the condenser. The current which is flowing through the inductor when one-third of the total energy is in the magnetic field of the inductor is
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Electric Field LinesAn electric field line in general is a curve drawn in such a way that the tangent to it at each point is in the direction of the electric field at that point. A field line is a space curve, i.e. a curve in three dimensions. Electric field lines are thus used to pictorially map the electric field around a charge or a configuration of charges.The density of field lines is more near the charge. Away from the charge, the field is weak, so the density of field lines is less.The spacing between two electric field lines indicates
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Assertion: At the centre of the line joining two equal and opposite charges, `E = 0`. Reason: At the centre of the line joining two equal and similar charge, `E !=
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A charged metallic sphere A is suspended by a nylon thread. Another charged metallic sphere B held by an insulating handle is brought close to A such that the distance between their centres is 10 cm, as shown in Fig. (a). The resulting repulsion of A is noted (for example, by shining a beam of light and measuring the deflection of its shadow on a screen). Spheres A and B are touched by uncharged spheres C and D respectively, as shown in Fig. (b). C and D are then removed and B is brought closer to A to a distance
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Cavendish’s ExperimentThe figure shows the schematic drawing of Cavendish’s experiment to determine the value of the gravitational constant. The bar AB has two small lead spheres attached at its ends. The bar is suspended from a rigid support by a fine wire.Two large lead spheres are brought close to the small ones but on opposite sides as shown. The value of G from this experiment came to be `6.67 xx 10^(-11) N-m^2'/'kg^2`.After Cavendish’s experiment, there have been given suggestions that the value of the gravitational constant G becomes smaller when considered over very large time period (in billions of years)
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In the figure, the net electric flux through the area A is `phi=vecE.vecA` when the system is in air. On immersing the system in water the net electric flux through the
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