Some physical constants are given in List - I and their dimensional formulae are given in List - II. Match the following :
List - I List - II
A) Planck's constant e) $[{M L}^{- 1} T^{- 2}]$
B) Gravitational constant f) $[{M L}^{1} T^{- 1}]$
C) Bulk modulus g) $[{M L}^{2} T^{- 1}]$
D) Linear momentum h) $[M^{- 1} L^{3} T^{- 2}]$

A-h, B-g, C-e ,D-f

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A-f, B-e, C-g, D-h

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A-g, B-f, C-e, D-h

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A-g, B-h, C-e, D-f

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Solution

The correct option is C A-g, B-h, C-e, D-f
Planck's constant $= \frac{(e n e r g y)}{(c / λ)} = \frac{M L^{2} T^{- 2}}{\frac{L T^{- 1}}{L}} = M L^{2} T^{- 1}$
Gravitational constant $= \frac{f o r c e}{(M_{1} M_{2})} \times r^{2} = \frac{M L^{1} T^{- 2} \times L^{2}}{M^{2}}$ $= M^{- 1} L^{3} T^{- 2}$

Bulk modulus $= \frac{d p}{d v / v} = \frac{M^{1} L^{- 1} T^{- 2}}{L^{3} / L^{3}} = M^{1} L^{- 1} T^{- 2}$

Linear momentum $= M L T^{- 1}$
Hence, option D is correct.

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Similar questions

Q. Names of units of some physical quantities are given in List - I and their dimensional formulae are given in List - II. Match the correct pair of the lists.

List - I	List - II
a) Pa-s	e) $[L^{2} T^{- 2} K^{- 1}]$
b) ${N m K}^{- 1}$	f) ${M L T}^{- 3} K^{- 1}$
c) ${J k g}^{- 1} k^{- 1}$	g) ${M L}^{- 1} T^{- 1}$
d) ${W m}^{- 1} k^{- 1}$	h) $[{M L}^{2} T^{- 2} K^{- 1}]$

Match the items in the second list with corresponding items from the first list

$\begin{matrix} L i s t I & L i s t I I (A) & V a r i a t i o n o f g w i t h h e i g h t (f o r a n y h e i g h t) & e & g^{'} = g (1 - \frac{2 h}{R}) (B) & V a r i a t i o n o f g w i t h h e i g h t (f o r s m a l l h e i g h t s h << R) & f & \frac{G M}{R^{2}} (C) & V a r i a t i o n o f g w i t h d e p t h & g & g^{'} = \frac{g R^{2}}{(R + h)^{2}} (D) & g o n t h e s u r f a c e o f t h e p l a n e t & h & g^{'} = g (1 - \frac{d}{R}) \end{matrix}$

Match List I with List II

List-I List-II

a) Dalton's Law e) PV= constant (T = constant)

b) Charle's Law-I f) P/T = constant (V = constant)

c) Charle's Law-II g) V/T= constant (P = constant)

d) Boyle's Law h) P = $P_{1} + P_{2} + . . . . . . P_{\infty}$

Q. A man of mass

m

stands on a weighing machine in a lift

\begin{matrix} List-I & List-II Lift moves & reading of machine a) up with uniform acceleration ' a' & e) m g b) down with uniform acceleration ' a' & f) m (g + a) c) down with uniform velocity & g) m (g - a) d) freely falling lift & h) 0 \end{matrix}

Match the items in the second list with corresponding items from the first list

$\begin{matrix} L i s t I & L i s t I I (A) & P e r f e c t g a s e q u a t i o n i s & e & \frac{R}{N} (B) & B o l t m a n n^{'} s c o n s t a n t, K_{B} & f & \frac{M o l e c u l a r m a s s}{M a s s o f 1 m o l e c u l e} (C) & A v o g a d r o^{'} s n u m b e r & g & P V = n R T (D) & N o . o f m o l e s, n = & h & \frac{M a s s o f g a s}{M o l e c u l a r m a s s} \end{matrix}$

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List - I	List - II
A) Planck's constant	e) $[{M L}^{- 1} T^{- 2}]$
B) Gravitational constant	f) $[{M L}^{1} T^{- 1}]$
C) Bulk modulus	g) $[{M L}^{2} T^{- 1}]$
D) Linear momentum	h) $[M^{- 1} L^{3} T^{- 2}]$

Some physical constants are given in List - I and their dimensional formulae are given in List - II. Match the following :List - IList - IIA) Planck's constante) [ML−1T−2]B) Gravitational constantf) [ML1T−1]C) Bulk modulusg) [ML2T−1]D) Linear momentumh) [M−1L3T−2]

The correct option is C A-g, B-h, C-e, D-fPlanck's constant =(energy)(c/λ)=ML2T−2LT−1L=ML2T−1Gravitational constant =force(M1M2)×r2=ML1T−2×L2M2=M−1L3T−2Bulk modulus =dpdv/v=M1L−1T−2L3/L3=M1L−1T−2Linear momentum =MLT−1Hence, option D is correct.