Match Physical Quantities with Dimensions Easily

 

❓ 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 Explanation

This problem is based on:

👉 Dimensional analysis
👉 Fundamental units
👉 Matching dimensions.

Main idea:

Convert every physical quantity into:

$$[M^aL^bT^c]$$

form and compare.

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🔷 Step 1 — Mass Density 💯

Mass density:

$$\rho=\frac{\text{mass}}{\text{volume}}$$

Dimensions:

$$=\frac{M}{L^3}$$
$$\boxed{ [ML^{-3}] }$$

Thus:

$$(A)\rightarrow(IV)$$

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🔷 Step 2 — Impulse

Impulse:

$$=\text{Force}\times\text{time}$$

Force dimensions:

$$[MLT^{-2}]$$

Multiply by time:

$$[MLT^{-2}]\times[T]$$
$$\boxed{ [MLT^{-1}] }$$

Thus:

$$(B)\rightarrow(II)$$

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🔷 Step 3 — Power

Power:

$$=\frac{\text{work}}{\text{time}}$$

Work dimensions:

$$[ML^2T^{-2}]$$

Divide by time:

$$\boxed{ [ML^2T^{-3}] }$$

Thus:

$$(C)\rightarrow(I)$$

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🔷 Step 4 — Moment of Inertia

Moment of inertia:

$$I=mr^2$$

Dimensions:

$$[M]\times[L^2]$$
$$\boxed{ [ML^2] }$$

Thus:

$$(D)\rightarrow(III)$$

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🔷 Step 5 — Final Matching

$$(A)\rightarrow(IV)$$
$$(B)\rightarrow(II)$$
$$(C)\rightarrow(I)$$
$$(D)\rightarrow(III)$$

This corresponds to:

$$\boxed{ \text{Option 4} }$$

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🔷 Step 6 — JEE Trap Alert 🚨

❌ Impulse aur force dimensions same maan lena

❌ Power me time division bhool jaana

❌ Density me $L^{-3}$ miss kar dena

Remember:

Density

$$\boxed{ \frac{M}{L^3} }$$

Power

$$\boxed{ \frac{\text{Energy}}{\text{time}} }$$

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✅ Final Answer

$$\boxed{ (A)-(IV),\ (B)-(II),\ (C)-(I),\ (D)-(III) }$$

(Option 4)

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