Out of the following, the only pair that does not have identical dimensions is

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Accepted Answer

To find the pair with non-identical dimensions, we analyze the dimensional formula for each quantity using the NCERT Appendix:

1.  **Angular Momentum and Planck's Constant:**
    *   Angular Momentum ($L = mvr$): Dimensions are $[ML^2T^{-1}]$ .
    *   Planck's Constant ($h = E/
u$): Dimensions are $[ML^2T^{-1}]$ .
    *   *Result:* Identical.

2.  **Moment of Inertia and Moment of a Force:**
    *   **Moment of Inertia ($I = mr^2$):** Dimensions are $[M][L]^2 = [ML^2]$ .
    *   **Moment of a Force (Torque, $	au = r 	imes F$):** Dimensions are $[L][MLT^{-2}] = [ML^2T^{-2}]$ .
    *   *Result:* **Not Identical** ($[ML^2] 
eq [ML^2T^{-2}]$).

3.  **Work and Torque:**
    *   Work ($W = F \cdot d$): Dimensions are $[ML^2T^{-2}]$ .
    *   Torque: Dimensions are $[ML^2T^{-2}]$ .
    *   *Result:* Identical.

4.  **Impulse and Momentum:**
    *   Impulse ($I = F 	imes t$): Dimensions are $[MLT^{-2}][T] = [MLT^{-1}]$ .
    *   Momentum ($p = mv$): Dimensions are $[M][LT^{-1}] = [MLT^{-1}]$ .
    *   *Result:* Identical.

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