IIT-JEE 2007 · Paper 1 · Physics Q20

PhysicsMatrix match+6Question 20 of 66

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

A
$GM_eM_s$ ( $G$ - universal gravitational constant, $M_e$ - mass of the earth, $M_s$ - mass of the Sun)
B
$\dfrac{3RT}{M}$ ( $R$ - universal gas constant, $T$ - absolute temperature, $M$ - molar mass)
C
$\dfrac{F^2}{q^2B^2}$ ( $F$ - force, $q$ - charge, $B$ - magnetic field)
D
$\dfrac{GM_e}{R_e}$ ( $G$ - universal gravitational constant, $M_e$ - mass of the earth, $R_e$ - radius of the earth)

Column II

P
(volt) (coulomb) (metre)
Q
(kilogram) (metre)³ (second)⁻²
R
(metre)² (second)⁻²
S
(farad) (volt)² (kg)⁻¹

Answer and worked solution

Official answer: A → P, Q; B → R, S; C → R, S; D → R, S

A, $GM_eM_s$ : $G\frac{Mm}{r^2}$ is a force, so $GMm$ has units N m² = kg m³ s⁻². Also (volt)(coulomb)(metre) = J m = N m². → P, Q.
B, $\frac{3RT}M$ : the square of the rms speed, m² s⁻². Also $\frac{CV^2}{\text{kg}}$ = J/kg = m² s⁻². → R, S.
C, $\frac{F^2}{q^2B^2}$ : $F=qvB$ , so this is $v^2$ : m² s⁻². → R, S.
D, $\frac{GM_e}{R_e}$ : $=gR_e$ , also a squared speed. → R, S.

Answer: A → P, Q; B → R, S; C → R, S; D → R, S

Topics:Dimensional analysis

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IIT-JEE 2007 · Paper 1, Physics question 20