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  • Question 1
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    The Van der Waal's equation of state for some gases can be expressed as:
    $$(P + \dfrac{a}{V^2})(V - b) = RT$$
    where P is the pressure, V is the molar volume, and T is the absolute temperature of the given sample of gas and a,b and R are constants.
    The dimensions of a are

  • Question 2
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    Dimensions of $$\dfrac {1}{\mu_{0}\epsilon_{0}}$$, where symbols have their usual meaning, are:

  • Question 3
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    The dimension of magnetic field in $$M, L, T$$ and $$C$$ (Coulomb) is given as:

  • Question 4
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    In terms of resistance $$R$$ and time $$T$$, the dimensions of ratio $$\dfrac {\mu}{\epsilon}$$ of the permeability $$\mu$$ and permittivity $$\epsilon$$ is:

  • Question 5
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    A vernier callipers has its main scale of $$10 cm$$ equally divided into $$200$$ equal parts. Its vernier scale of $$25$$ divisions coincides with $$12 mm$$ on the main scale. The least count of the instrument is - 

  • Question 6
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    The dimensions of angular momentum, latent heat and capacitance are, respectively.

  • Question 7
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    The dimension of electrical conductivity is _________.

  • Question 8
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    Match the physical quantities given in Column I with dimensions expressed in terms of mass (M), length (L) time (T), and charge (Q) given in Column II.

    Column IColumn II
    i. Angular momentuma. $$ML^2T^{-2}$$
    ii. Torqueb. $$ML^2T^{-1}$$
    iii. Inductancec. $$M^{-1}L^{-2}T^2Q^2$$
    iv. Latent heatd. $$ML^2Q^{-2}$$
    v. Capacitancee. $$ML^3T^{-1}Q^{-2}$$
    vi. Resistivityf. $$L^2T^{-2}$$

  • Question 9
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    The dimension of permittivity of vacuum 

  • Question 10
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    Two particles of mass $${m}_{1}$$ and $${m}_{2}$$ are approaching towards each other under their mutual gravitational field. If the speed of the particle is $$v$$, the speed of the center of mass of the system is equal to:

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