Some physical quantities are given in Column I and some possible SI units in which these quantities may be expressed are given in Column II. Match the physical quantities in Column I with the units in Column II and indicate your answer by darkening appropriate bubbles in the 4 × 4 matrix given in the ORS. | Column I | Column II | | --- | --- | | (A) $G M_{e} M_{s}$ $G$ - universal gravitational constant, $M_{e}$ - mass of the earth, $M_{s}$ - mass of the Sun | (p) (volt) (coulomb) (metre) | | (B) $\frac{3 R T}{M}$ $R$ - universal gas constant, $T$ - absolute temperature, $M$ - molar mass | (q) (kilogram) (metre)$^{3}$ (second)$^{-2}$ | | (C) $\frac{F^{2}}{q^{2} B^{2}}$ $F$ - force, $q$ - charge, $B$ - magnetic field | (r) (metre)$^{2}$ (second)$^{-2}$ | | (D) $\frac{G M_{e}}{R_{e}}$ $G$ - universal gravitational constant, $M_{e}$ - mass of the earth, $R_{e}$ - radius of the earth | (s) (farad) (volt)$^{2}$ (kg)$^{-1}$ |

**(A) :** Dimensions are . This matches (p) (volt)(coulomb)(metre) = (J/C)(C)(m) = J·m = kg·m³·s⁻² and (q) directly. **(B) :** Dimensions are , which is (velocity)². This matches (r) m²s⁻² and (s) (farad)(volt)²(kg)⁻¹ = (C²/J)(J²/C²)(kg⁻¹) = J·kg⁻¹ = m²s⁻². **(C) :** Dimensions are . Matches (r) an…

Units & Measurement — JEE Advanced · 2007 · 08 Apr 2007 · Paper 1 Question with Solution

Some physical quantities are given in Column I and some possible SI units in which these quantities may be expressed are given in Column II. Match the physical quantities in Column I with the units in Column II and indicate your answer by darkening appropriate bubbles in the 4 × 4 matrix given in the ORS.

Column I	Column II
(A) $G M_{e} M_{s}$ <br> $G$ - universal gravitational constant,<br> $M_{e}$ - mass of the earth,<br> $M_{s}$ - mass of the Sun	(p) (volt) (coulomb) (metre)
(B) $\frac{3 R T}{M}$ <br> $R$ - universal gas constant,<br> $T$ - absolute temperature,<br> $M$ - molar mass	(q) (kilogram) (metre) $^{3}$ (second) $^{- 2}$
(C) $\frac{F ^{2}}{q ^{2} B ^{2}}$ <br> $F$ - force,<br> $q$ - charge,<br> $B$ - magnetic field	(r) (metre) $^{2}$ (second) $^{- 2}$
(D) $\frac{G M _{e}}{R _{e}}$ <br> $G$ - universal gravitational constant,<br> $M_{e}$ - mass of the earth,<br> $R_{e}$ - radius of the earth	(s) (farad) (volt) $^{2}$ (kg) $^{- 1}$

Answer: A → I, A → II, B → III, B → IV, C → III, C → IV, D → III, D → IV

Solution

**(A)

G M_{e} M_{s}

:** Dimensions are

[G] [M] [M] = [L^{3} M^{- 1} T^{- 2}] [M] [M] = [M L^{3} T^{- 2}]

. This matches (p) (volt)(coulomb)(metre) = (J/C)(C)(m) = J·m = kg·m³·s⁻² and (q) directly.

**(B)

\frac{3 R T}{M}

:** Dimensions are

[R] [T] / [M] = [M L^{2} T^{- 2} K^{- 1} m o l^{- 1}] [K] / [M k m o l^{- 1}] = [L^{2} T^{- 2}]

, which is (velocity)². This matches (r) m²s⁻² and (s) (farad)(volt)²(kg)⁻¹ = (C²/J)(J²/C²)(kg⁻¹) = J·kg⁻¹ = m²s⁻².

**(C)

\frac{F ^{2}}{q ^{2} B ^{2}}

:** Dimensions are

[F]^{2} / ([q]^{2} [B]^{2}) = [M L T^{- 2}]^{2} / ([A T]^{2} [M T^{- 2} A^{- 1}]^{2}) = [M^{2} L^{2} T^{- 4}] / [M^{2} T^{- 2}] = [L^{2} T^{- 2}]

. Matches (r) and (s).

**(D)

\frac{G M _{e}}{R _{e}}

:** Dimensions are

[G] [M] / [L] = [L^{3} M^{- 1} T^{- 2}] [M] / [L] = [L^{2} T^{- 2}]

. Matches (r) and (s).

Pairs: A→(p),(q); B→(r),(s); C→(r),(s); D→(r),(s).

JEE Advanced · 2007 · 08 Apr 2007 · Paper 1 · Match the columns

JEE Advanced · 2007 · 08 Apr 2007 · Paper 1 · Units & Measurement

Solution

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