In a typical combustion engine the work done by a gas molecule is given $W =\alpha^{2} \beta e ^{\frac{-\beta x ^{2}}{ KT }}$, where $x$ is the displacement, $k$ is the Boltzmann constant and $T$ is the temperature. If $\alpha$ and $\beta$ are constants, dimensions of $\alpha$ will be
  • A$\left[ MLT ^{-2}\right]$
  • B$\left[ M ^{0} LT ^{0}\right]$
  • C$\left[ M ^{2} LT ^{-2}\right]$
  • D$\left[ MLT ^{-1}\right]$
JEE MAIN 2021, Diffcult
art

Download our app
and get started for free

Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*

Similar Questions

  • 1
    Which of the following is a dimension of volt 
    View Solution
  • 2
    Match List - $I$ with List - $II$.

    List - $I$  $(Number)$   $List - II$  $(Significant figure)$
    $(A)$ $1001$     $(I)$ $3$
    $(B)$ $010.1$    $(II)$ $4$
    $(C)$ $100.100$  $(III)$ $5$
    $(D)$ $0.0010010$ $(IV)$ $6$

    Choose the correct answer from the options given below :

    View Solution
  • 3
    With the usual notations, the following equation ${S_t} = u + \frac{1}{2}a(2t - 1)$ is
    View Solution
  • 4
    The internal and external radii of a hollow cylinder are measured with the help of a vernier callipers.Their values are $(4.23 \pm 0.01)\,\,cm$ and $(3.87 \pm 0.01)\,\,cm,$ respectively. The thickness of the wall of the cylinder is
    View Solution
  • 5
    A screw gauge gives the following reading when used to measure the diameter of a wire.

    Main scale reading : $0\ mm$

    Circular scale reading : $52\ divisions$

    Given that $1\ mm$ on main scale corresponds to $100$ divisions of the circular scale. The diameter of wire from the above data is:

    View Solution
  • 6
    The area of a square is $5.29 \ cm^2$. The area of $7$ such squares taking into account the significant figures is $........... cm^2$
    View Solution
  • 7
    If $L , C$ and $R$ are the self inductance, capacitance and resistance respectively, which of the following does not have the dimension of time?
    View Solution
  • 8
    The maximum percentage errors in the measurement of mass (M), radius (R) and angular velocity $(\omega)$ of a ring are $2 \%, 1 \%$ and $1 \%$ respectively, then find the maximum percenta? error in the measurement of its rotational kinetic energy $\left(K=\frac{1}{2} I \omega^{2}\right)$
    View Solution
  • 9
    Dimensional formula for pressure head is ............
    View Solution
  • 10
    In Ohm's experiment, the value of an unknown resistance were found to be $4.12\; \Omega, 4.08 \;\Omega, 4.22 \;\Omega$ and $4.14 \;\Omega$. Calculate absolute error and relative error in these measurement.
    View Solution