JEE MAIN - Physics (2023 - 29th January Morning Shift - No. 9)
Match List I with List II :
| List I (Physical Quantity) | List II (Dimensional Formula) | ||
|---|---|---|---|
| A. | Pressure gradient | I. | $$\left[\mathrm{M}^{\circ} \mathrm{L}^{2} \mathrm{~T}^{-2}\right]$$ |
| B. | Energy density | II. | $$\left[\mathrm{M}^{1} \mathrm{L}^{-1} \mathrm{~T}^{-2}\right]$$ |
| C. | Electric Field | III. | $$\left[\mathrm{M}^{1} \mathrm{L}^{-2} \mathrm{~T}^{-2}\right]$$ |
| D. | Latent heat | IV. | $$\left[\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-3} \mathrm{~A}^{-1}\right]$$ |
Choose the correct answer from the options given below:
A-III, B-II, C-IV, D-I
A-III, B-II, C-I, D-IV
A-II, B-III, C-IV, D-I
A-II, B-III, C-I, D-IV
Explanation
Pressure gradient $=\frac{d p}{d x}=\frac{\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]}{[\mathrm{L}]}$
$$ =\left[\mathrm{M}^{1} \mathrm{~L}^{-2} \mathrm{~T}^{-2}\right] $$
Energy density $=\frac{\text { energy }}{\text { volume }}=\frac{\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]}{\left[\mathrm{L}^{3}\right]}$
$$ =\left[\mathrm{M}^{1} \mathrm{~L}^{-1} \mathrm{~T}^{-2}\right] $$
Electric field $=\frac{\text { Force }}{\text { ch arge }}=\frac{\left[\text { MLT }^{-2}\right]}{[\text { A.T }]}$
$=\left[\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-3} \mathrm{~A}^{-1}\right]$
Latent heat $=\frac{\text { heat }}{\text { mass }}=\frac{\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]}{[\mathrm{M}]}$
$=\left[\mathrm{M}^{0} \mathrm{~L}^{2} \mathrm{~T}^{-2}\right]$
$$ =\left[\mathrm{M}^{1} \mathrm{~L}^{-2} \mathrm{~T}^{-2}\right] $$
Energy density $=\frac{\text { energy }}{\text { volume }}=\frac{\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]}{\left[\mathrm{L}^{3}\right]}$
$$ =\left[\mathrm{M}^{1} \mathrm{~L}^{-1} \mathrm{~T}^{-2}\right] $$
Electric field $=\frac{\text { Force }}{\text { ch arge }}=\frac{\left[\text { MLT }^{-2}\right]}{[\text { A.T }]}$
$=\left[\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-3} \mathrm{~A}^{-1}\right]$
Latent heat $=\frac{\text { heat }}{\text { mass }}=\frac{\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]}{[\mathrm{M}]}$
$=\left[\mathrm{M}^{0} \mathrm{~L}^{2} \mathrm{~T}^{-2}\right]$
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