Match List - I with List - II.
List - I                            List - II
(a) Torque                    (i) MLT$$^{-1}$$
(b) Impulse                  (ii) MT$$^{-2}$$
(c) Tension                  (iii) ML$$^2$$ T$$^{-2}$$
(d) Surface Tension     (iv) MLT$$^{-2}$$
Choose the most appropriate answer from the option given below:

We start by recalling that in dimensional analysis we express any physical quantity in terms of the fundamental dimensions: mass $$M$$, length $$L$$ and time $$T$$. The exponents of these symbols tell us how the quantity depends on each fundamental dimension.

For torque we use the definition “torque = force × perpendicular distance.” First we write the dimensional formula of force. From Newton’s second law, “force = mass × acceleration,” and acceleration is “length / time2.” Hence

$$[\text{Force}] = M^1L^1T^{-2}.$$

Multiplying by distance (another factor of $$L$$) gives

$$[\text{Torque}] = M^1L^1T^{-2}\; \times \; L^1 = M^1L^{1+1}T^{-2} = ML^{2}T^{-2}.$$

So torque corresponds to $$ML^{2}T^{-2},$$ which is entry (iii).

For impulse we recall the relation “impulse = force × time.” Stating the dimensional formula once more, force is $$MLT^{-2}$$ and time is $$T^1$$. Hence

$$[\text{Impulse}] = (MLT^{-2}) \times (T^1) = ML\,T^{-2+1} = MLT^{-1}.$$

Thus impulse matches $$MLT^{-1},$$ which is entry (i).

For tension we simply note that tension is a kind of force (a pulling force in a string). Therefore its dimensional formula is identical to that of force:

$$[\text{Tension}] = MLT^{-2}.$$

This equals entry (iv).

For surface tension we remember the definition “surface tension = force per unit length.” We again insert the force dimension $$MLT^{-2}$$ and divide by length $$L^1$$:

$$[\text{Surface Tension}] = \dfrac{MLT^{-2}}{L} = MT^{-2}.$$

This matches entry (ii).

Collecting all the matches, we have

$$(a) \longrightarrow (iii), \quad (b) \longrightarrow (i), \quad (c) \longrightarrow (iv), \quad (d) \longrightarrow (ii).$$

Comparing with the options supplied, we see that Option B lists exactly this set of pairings.

Hence, the correct answer is Option B.