The work done by a gas molecule in an isolated system is given by $W=\alpha {\beta }^2{e}^{-\frac{x^2}{\alpha kT}}$ , where x is the displacement, k is the Boltzmann constant and T is the temperature. a and b are constants. Then the dimensions of b will be:

An expression for a dimensionless quantity P is given by $P=\frac{\alpha }{\beta }lo{g}_e\left(\frac{kt}{\beta t}\right);$  where a and b are constants, x is distance; k is Boltzmann constant and t is the temperature. Then the dimensions of a will be:

If velocity [V], time [T] and force [F] are chosen as the base quantities, the dimensions of the mass will be:

If mass M, area A' and velocity V are chosen as fundamental units, then the dimension of coefficient of viscosity will be:
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If E and G respectively denotes energy and gravitational constant, then E/G has the dimensions of:

A quantity X is given by (IFv²MLL⁴) in terms of moment of inertia I, force F, velocity v, work W and Length L. The dimensional formula for x is same as that of:
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