1

IIT-JEE 1997

Fill in the Blanks
The equation of state for real gas is given by $$\left( {P + {a \over {{V^2}}}} \right)\left( {V - b} \right) = RT$$. The dimention of the constant a is ___________.

Answer

ML5T-2

Explanation

$$\left[ {{a \over {{V^2}}}} \right] = \left[ P \right]$$
$$\therefore \left[ a \right] = \left[ {P{V^2}} \right]$$
$$ = {{ML{T^{ - 2}}} \over {{L^2}}}{L^6} = M{L^5}{T^{ - 2}}$$
2

IIT-JEE 1988

Fill in the Blanks
In the formula X = 3YZ2, X and Z have dimensions of capacitance and magnetic induction respectively. The dimensions of Y in MKSQ system are _____________

Answer

$$\left[M^{-3}L^{-2}T^4Q^4\right]$$

Explanation

$$\begin{array}{l}\begin{array}{l}\left[X\right]\;=\;\left[C\right]\;=\;\left[M^{-1}L^{-2}T^2Q^2\right]\\\left[Z\right]\;=\;\left[B\right]\;=\;\left[MT^{-1}Q^{-1}\right]\\\\\Rightarrow\;\left[Y\right]\;=\;\frac{\;\left[M^{-1}L^{-2}T^2Q^2\right]}{\;\left[MT^{-1}Q^{-1}\right]^2}\;\end{array}\\\\=\;\left[M^{-3}L^{-2}T^4Q^4\right]\\\\\\\\\\\end{array}$$
3

IIT-JEE 1985

Fill in the Blanks
Plank' constant has dimension __________.

Answer

ML2T-1

Explanation

We know E = hv
So $$h = {E \over v} = {{\left[ {M{L^2}{T^{ - 2}}} \right]} \over {\left[ {{T^{ - 1}}} \right]}} = \left[ {M{L^2}{T^{ - 1}}} \right]$$

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