Match List I with List II. List I List II (A) Young's Modulus (I) (B) Torque (II) (C) Coefficient of Viscosity (III) (D) Gravitational Constant (IV) Choose the correct answer from the options given below : [2025]

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Solution

Q.
Match List I with List II.

List I List II

(A) Young's Modulus (I) $M L^{- 1} T^{- 1}$

(B) Torque (II) $M L^{- 1} T^{- 2}$

(C) Coefficient of Viscosity (III) $M^{- 1} L^{3} T^{- 2}$

(D) Gravitational Constant (IV) $M L^{2} T^{- 2}$

Choose the correct answer from the options given below : [2025]

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

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

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

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

Ans.
(4)

(A) $[Y] = \frac{F}{A (\frac{△ l}{l})} \Rightarrow \frac{M L T^{- 2}}{L^{2}} = M L^{- 1} T^{- 2}$

(B) Torque $(\vec{τ}) = \vec{r} \times \vec{F} = L \times M L T^{- 2} = M L^{2} T^{- 2}$

(C) Coefficient of viscosity $\Rightarrow F = η A \frac{d V}{d t}$

   $[η] = \frac{M L T^{- 2}}{L^{2}} \times T = M L^{- 1} T^{- 1}$

(D) Gravitational constant (G)

   $F = \frac{G M_{1} M_{2}}{r^{2}}$

   $[G] = \frac{F \cdot r^{2}}{m_{1} m_{2}} = \frac{M L T^{- 2} \times L^{2}}{M^{2}} = M^{- 1} L^{3} T^{- 2}$

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