Which Pair Has Different Dimensions JEE Main PYQ

 

❓ Question

The pair of physical quantities not having the same dimensions is:

1. Pressure & Young's Modulus
2. Surface Tension & Impulse
3. Torque & Energy
4. Angular Momentum & Planck's Constant

---

✍️ Solution

(1) Pressure & Young's Modulus

Pressure is

$$P=\frac{F}{A}$$
$$[P]=\frac{[MLT^{-2}]}{[L^2]}$$
$$\boxed{[P]=[ML^{-1}T^{-2}]}$$

Young's modulus is

$$Y=\frac{\text{Stress}}{\text{Strain}}$$

Since strain is dimensionless,

$$\boxed{[Y]=[ML^{-1}T^{-2}]}$$

Thus, both have the same dimensions.

---

(2) Surface Tension & Impulse

Surface tension is

$$T=\frac{F}{l}$$
$$[T]=\frac{[MLT^{-2}]}{[L]}$$
$$\boxed{[T]=[MT^{-2}]}$$

Impulse is

$$J=F\times t$$
$$[J]=[MLT^{-2}][T]$$
$$\boxed{[J]=[MLT^{-1}]}$$

Thus, they do not have the same dimensions.

$$\boxed{\text{Option 2}}$$

---

(3) Torque & Energy

Torque is

$$\tau=F\times r$$
$$[\tau]=[MLT^{-2}][L]$$
$$\boxed{[\tau]=[ML^2T^{-2}]}$$

Energy is

$$E=F\times d$$
$$\boxed{[E]=[ML^2T^{-2}]}$$

Thus, both have the same dimensions.

---

(4) Angular Momentum & Planck's Constant

Angular momentum is

$$L=mvr$$
$$[L]=[M][LT^{-1}][L]$$
$$\boxed{[L]=[ML^2T^{-1}]}$$

From

$$E=h\nu$$
$$h=\frac{E}{\nu}$$
$$[h]=\frac{[ML^2T^{-2}]}{[T^{-1}]}$$
$$\boxed{[h]=[ML^2T^{-1}]}$$

Thus, both have the same dimensions.

---

✅ Final Answer

$$\boxed{\text{Option 2 — Surface Tension \& Impulse}}$$