CBSE [All India]-Set-3-2010

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  • Q1

    A converging lens is kept coaxially in contact with a diverging lens – both the lenses being of equal focal lengths. What is the focal length of the combination?

    Marks:1
    Answer:

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  • Q2

    Define self-inductance of a coil. Write its S.I. units.

    Marks:1
    Answer:

    Self inductance of a coil is defined as the induced e.m.f. produced in the coil through which the rate of change of current is unity. Its S.I. unit is henry (denoted by H).

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  • Q3

    Two conducting wires X and Y of same diameter but different material are joined in series across a battery. If the number density of electron in X is twice that in Y, find the ratio of drift velocity of electrons in the two wires.

    Marks:1
    Answer:

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  • Q4

    Define ionisation energy. What is its value for a hydrogen atom?

    Marks:1
    Answer:

    The minimum energy required to knock an electron (from its ground state) completely out of an atom is known as ionisation energy. For, hydrogen atom, it is 13.6 eV.

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  • Q5

    Name the part of electromagnetic spectrum whose wavelength lies in the range of 10-10 m. Give its one use.

    Marks:1
    Answer:

    The wavelength of X-rays is of the order of 10-10 m. X-rays are used as a diagnostic tool in medicine and as a treatment for certain forms of cancer.

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  • Q6

    1. A beam of protons projected along + x-axis, experiences a force due to a magnetic field along the -y-axis. What is the direction of the magnetic field?

    Marks:1
    Answer:

    Therefore, according to Right Hand Rule, the magnetic field is directed along the +z-direction.

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  • Q7

    When light travels from a rarer to a denser medium, the speed decreases. Does this decrease in speed imply a decrease in the energy carried by the light wave? Justify your answer.

    Marks:1
    Answer:

    No, the decrease in speed of light wave on travelling from a rarer to a denser medium does not imply a decrease in its energy.
    The frequency of light wave remains unchanged on passing from one medium to another. Since 
     is the frequency, the energy remains constant.

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  • Q8

    The ground state energy of hydrogen atom is -13.6 eV. What are the kinetic and potential energies of electron in this state?

    Marks:1
    Answer:

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  • Q9

    Draw a plot of the binding energy per nucleon as a function of mass number for a large number of nuclei, 2  A   240. How do you explain the constancy of binding energy per nucleon in the range 30 < A< 170 using the property that nuclear force is short-ranged?

    Marks:2
    Answer:

    A plot of the binding energy per nucleon as a function of mass number for a large number of nuclei, 2  A  240 is given below.

     

    The constancy of the binding energy in the range 30 < A< 170 is because of the fact that the nuclear force is short ranged. A nucleon inside a nucleus will be under the influence of only some of its neighbours, which come within the range of nuclear force. The binding energy of a nucleon is proportional to the maximum number of neighbouring nucleons within the range of nuclear force. If we increase A by adding nucleons, they will not change the B.E. of a nucleon inside. Since most of the nucleons in a large nucleus (in the range of 30 < A< 170) reside inside it and not on the surface, the change in the binding energy would be small.

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  • Q10

    Show that the electric field at the surface of a charged conductor is given by , where is the surface charge density and is a unit vector normal to the surface in the outward direction. the infinitesimal plane sheet and is directed outward direction.

    Marks:2
    Answer:

    We can consider an infinitesimally small part of the surface of the charged conductor as a plane sheet of uniform charge density . Let us consider a cylindrical Gaussain surface of cross section A, as shown in the figure below:

    Now, by Gauss’ theorem,


    Since the electric field is perpendicular to the infinitesimal plane sheet and is directed outward,

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