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Physics · Units, Dimensions & Error Analysis

JEE Main 2025 — 29 January, Evening Shift — Question 32

Match List-I with List-II.

List-IList-II
(A)Young's Modulus(I)ML−1  ⁣ ⁣  ⁣ ⁣ T−1\text{M}{{\text{L}}^{-1}}\text{ }\!\!~\!\!\text{ }{{\text{T}}^{-1}}
(B)Torque(II)ML−1  ⁣ ⁣  ⁣ ⁣ T−2\text{M}{{\text{L}}^{-1}}\text{ }\!\!~\!\!\text{ }{{\text{T}}^{-2}}
(C)Coefficient of Viscosity(III)M−1  ⁣ ⁣  ⁣ ⁣ L3  ⁣ ⁣  ⁣ ⁣ T−2{{\text{M}}^{-1}}\text{ }\!\!~\!\!\text{ }{{\text{L}}^{3}}\text{ }\!\!~\!\!\text{ }{{\text{T}}^{-2}}
(D)Gravitational Constant(IV)ML2  ⁣ ⁣  ⁣ ⁣ T−2\text{M}{{\text{L}}^{2}}\text{ }\!\!~\!\!\text{ }{{\text{T}}^{-2}}

Choose the correct answer from the options given below :

  1. Option A:

    (A)-(I), (B)-(III), (C)-(II), (D)-(IV)

  2. Option B:

    (A)-(II), (B)-(I), (C)-(IV), (D)-(III)

  3. Option C:

    (A)-(IV), (B)-(II), (C)-(III), (D)-(I)

  4. Option D:

    (A)-(II), (B)-(IV), (C)-(I), (D)-(III)

    Correct

Answer: D

Step-by-step solution

(A) [Y]=FA(Δℓℓ)⇒MLT−2 L2=ML−1 T−2[\mathrm{Y}]=\frac{\mathrm{F}}{\mathrm{A}\left(\frac{\Delta \ell}{\ell}\right)} \Rightarrow \frac{\mathrm{MLT}^{-2}}{\mathrm{~L}^{2}}=\mathrm{ML}^{-1} \mathrm{~T}^{-2}

(II) (B) Torque (τ⃗)=r→×F→(\vec{\tau})=\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{F}} (τ⃗)=L×MLT−2=ML2 T−2(IV)(\vec{\tau})=\mathrm{L} \times \mathrm{MLT}^{-2}=\mathrm{ML}^{2} \mathrm{~T}^{-2}(\mathrm{IV})

(C) Coefficient of viscosity ⇒F=ηAdVdt\Rightarrow F=\eta A \frac{d V}{d t}

η→Pa⋅sec\eta \rightarrow \mathrm{Pa} \cdot \mathrm{sec}

[η]=MLT−2 L2×T=ML−1 T−1(I)[\eta]=\frac{\mathrm{MLT}^{-2}}{\mathrm{~L}^{2}} \times \mathrm{T}=\mathrm{ML}^{-1} \mathrm{~T}^{-1}(\mathrm{I}) (D) Gravitational constant

(G) F=GM1M2r2\mathrm{F}=\frac{\mathrm{GM}_{1} \mathrm{M}_{2}}{\mathrm{r}^{2}}

[G]=F⋅r2 m1 m2=MLT−2×L2M2=M−1 L3 T−2[\mathrm{G}]=\frac{\mathrm{F} \cdot \mathrm{r}^{2}}{\mathrm{~m}_{1} \mathrm{~m}_{2}}=\frac{\mathrm{MLT}^{-2} \times \mathrm{L}^{2}}{\mathrm{M}^{2}}=\mathrm{M}^{-1} \mathrm{~L}^{3} \mathrm{~T}^{-2} (III)

Answer key and solution verified before publishing.

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Exam
JEE Main 2025
Paper
29 January, Evening Shift
Subject
Physics
Chapter
Units, Dimensions & Error Analysis
Topic
Units and Dimensions Analysis

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