Dimensional Analysis & Its Applications

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  1. Dimensional analysis can be applied to
  2. $[MLT^{-1}] + [MLT^{-1}]$ =
  3. Two quantities A and B have same dimensions which mathematical operation given below is physically meaningful?
  4. Distance travelled by a particle at any instant ' t ' can be represented as $S = A(t + B) + Ct^{2}$. The dimensions of B are
  5. An expression for a dimensionless quantity P is given by $P = (\alpha/\beta)\log_{e}(kt/\beta x)$; where $\alpha$ and $\beta$ are constants, x is distance; k is Boltzmann constant and t is the temperature. Then the dimensions of $\alpha$ will be:
  6. If $v = a/t + bt^{3}$ where v = velocity and t is time The dimensional formula of a and b are
  7. A, B, C and D are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation $AD = C \ln (BD)$ holds true. Then which of the combination is not a meaningful quantity?
  8. The displacement of a body at a particular second n is given by the expression $S_{nth} = u + (a/2)(2n - 1)$. The dimensional formula of $S_{nth}$ in this equation is
  9. In Vander Waals equation $[P + a/V^{2}][V - b] = RT$; P is pressure, V is volume, R is universal gas constant and T is temperature. The ratio of constants $(a/b)$ is dimensionally equal to
  10. Write the dimensions of $a \times b$ in the relation $E = (b - x^{2})/(at)$, where E is the energy, x is the displacement and t is time
  11. What are the dimensions of $A/B$ in the relation $F = A\sqrt{x} + Bt^{2}$, where F is the force, x is the distance and t is time?
  12. A physical quantity x depends on quantities y and z as follows: $x = Ay + B \tan Cz$, where A, B and C are constants. Which of the following do not have the same dimensions:
  13. Which of the following equations is dimensionally incorrect? Where t = time, h = height, s = surface tension, $\theta$ = angle, $\rho$ = density, r = radius, $\xi$ = acceleration due to gravity, V = volume, P = pressure, W = work done, $\varepsilon$ = permittivity, E = electric field, J = current density, L = length, $\tau$ = torque
  14. If force (F), length (L) and time (T) are assumed to be fundamental units; then the dimensional formula of the mass will be