IIT-JEE-Physics-Mains-2002

3. A uniform solid cylinder of density 0.8 g/cm³ floats in equilibrium in a combination of two non-mixing liquids A and B with its axis vertical. The densities of the liquids A and B are 0.7 g/cm³ and 1.2 g/cm², respectively. The height of liquid A is h_A = 1.2 cm. The length of the part of the cylinder immersed in liquid B is
h_B = 0.8 cm.

uniform-solid-cylender

(a)       Find the total force exerted by liquid A on the cylinder.
(b)       Find h, the length of the part of the cylinder in air.
(c)        The cylinder is depressed in such a way that its top surface is just below the upper surface of liquid A and is then released. Find the acceleration of the cylinder immediately after it is released.

4.    A thin uniform wire AB of length 1 m, an unknown resistance X and a resistance of 12 W are connected by thick conducting strips, as shown in the figure. A battery and a galvanometer (with a sliding jockey connected to it) are also available. Connections are to be made to measure the unknown resistance X using the principle of Wheatstone bridge. Answer the following questions.

    uniform-wire

(a)       Are there positive and negative terminals on the galvanometer?
(b)       Copy the figure in your answer book and show the battery and the galvanometer (with jockey) connected at appropriate points.
(c)        After appropriate connections are made, it is found that no deflection takes place in the galvanometer when the sliding jockey touches the wire at a distance of 60 cm from A. Obtain the value of the resistance X.

5.         A hydrogen-like atom (described by the Bohr model) is observed to emit six wavelengths, originating from all possible transitions between a group of levels. These levels have energies between -0.85 eV and -0.544 eV (including both these values).
            (a)       Find the atomic number of the atom.
            (b)       Calculate the smallest wavelength emitted in these transitions.
            (Take hc = 1240 eV-nm, ground state energy of hydrogen atom = -13.6 eV.

6.         A point source S emitting light of wavelength 600 nm is placed at a very small height h above a flat reflecting surface AB (see figure). The intensity of the reflected light is 36% of the incident intensity. Interference fringes are observed on a screen placed parallel to the reflecting surface at a very large distance D from it.

   reflaction

(a)       What is the shape of the interference fringes on the screen?
(b)       Calculate the ratio of the minimum to the maximum intensities in the interference fringes formed near the point P (shown in the figure).
(c)        If the intensity at point P corresponds to a maximum, calculate the minimum distance through which the reflecting surface AB should be shifted so that the intensity at P again becomes maximum.

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