Match List - I with List - II.List - I(A) Mass density(B) Impulse(C) Power (D) Moment of inertiaList - II(I) [ML²T⁻³](II) [MLT⁻¹](III) [ML²T⁰](IV) [ML⁻³T⁰]

 

❓ Question

Match List - I with List - II:

List - I	List - II
(A) Mass density	(I) [ML²T⁻³]
(B) Impulse	(II) [MLT⁻¹]
(C) Power	(III) [ML²T⁰]
(D) Moment of inertia	(IV) [ML⁻³T⁰]

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🖼️ Question Image

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✍️ Short Solution

To solve this, recall the dimensional formulas for each physical quantity:

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Step 1 — Mass density (ρ)

Mass density is mass per unit volume:

$$\rho =\frac{M}{V}\Rightarrow [\rho ]=\frac{M}{L^3}=[M{L}^{-3}{T}^0]$$

✅ Match → (A) → (IV)

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Step 2 — Impulse (J)

Impulse is the product of force and time:

$$J=F\mathrm{\Delta }t=(ML{T}^{-2})(T)=[ML{T}^{-1}]$$

✅ Match → (B) → (II)

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Step 3 — Power (P)

Power is work done per unit time:

$$P=\frac{W}{t}=\frac{F\cdot L}{T}=\frac{(ML{T}^{-2})L}{T}=[M{L}^2{T}^{-3}]$$

✅ Match → (C) → (I)

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Step 4 — Moment of inertia (I)

Moment of inertia about an axis:

$$I=\sum m{r}^2\Rightarrow [I]=M{L}^2$$

✅ Match → (D) → (III)

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🧮 Image Solution

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✅ Conclusion & Video Solution

✅ Final Matching:

List - I	List - II
(A) Mass density	(IV) [M L⁻³ T⁰]
(B) Impulse	(II) [M L T⁻¹]
(C) Power	(I) [M L² T⁻³]
(D) Moment of inertia	(III) [M L² T⁰]

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Concept Recap:

• Mass density: mass per volume → [M L⁻³]

• Impulse: force × time → [M L T⁻¹]

• Power: work per time → [M L² T⁻³]

• Moment of inertia: Σ m r² → [M L²]