Match the List I with List II List I List II (A) Gravitational constant (I) [] (B) Gravitational potential energy (II) [] (C) Gravitational potential (III) [] (D) Acceleration due to gravity (IV) [] Choose the correct answer from the options given belo

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Q.
Match the List I with List II

List I List II

(A) Gravitational constant (I) [ $L T^{- 2}$ ]

(B) Gravitational potential energy (II) [ $L^{2} T^{- 2}$ ]

(C) Gravitational potential (III) [ $M L^{2} T^{- 2}$ ]

(D) Acceleration due to gravity (IV) [ $M^{- 1} L^{3} T^{- 2}$ ]

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

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

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

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

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

Ans.
(1)

(A) $G = \frac{F r^{2}}{m^{2}}$

$[G] = \frac{[M L T^{- 2}] [L^{2}]}{[M^{2}]} = [M^{- 1} L^{3} T^{- 2}] \Rightarrow A \to IV$

(B) P.E. $U = m g h = [M L T^{- 2} L] = [M L^{2} T^{- 2}] \Rightarrow B \to III$

(C) Gravitational Potential, $V = \frac{G M}{r}$

$V = \frac{[M^{- 1} L^{3} T^{- 2}] [M]}{[L]} = [M^{0} L^{2} T^{- 2}] = [L^{2} T^{- 2}] \Rightarrow C \to II$

(D) Acceleration due to gravity $= [g] = [L T^{- 2}] \Rightarrow D \to I$

Solution

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

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

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

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

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	List I		List II
(A)	Gravitational constant	(I)	[ $L T^{- 2}$ ]
(B)	Gravitational potential energy	(II)	[ $L^{2} T^{- 2}$ ]
(C)	Gravitational potential	(III)	[ $M L^{2} T^{- 2}$ ]
(D)	Acceleration due to gravity	(IV)	[ $M^{- 1} L^{3} T^{- 2}$ ]

Solution

Q. Match the List I with List II List I List II (A) Gravitational constant (I) [LT–2] (B) Gravitational potential energy (II) [L2T–2] (C) Gravitational potential (III) [ML2T–2] (D) Acceleration due to gravity (IV) [M–1L3T–2] Choose the correct answer from the options given below: [2025]

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

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

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

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

Ans. (1) (A) G=Fr2m2 [G]=[MLT–2][L2][M2]=[M–1L3T–2] ⇒ A→IV (B) P.E. U=mgh=[MLT–2L]=[ML2T–2] ⇒ B→III (C) Gravitational Potential, V=GMr V=[M–1L3T–2][M][L]=[M0L2T–2]=[L2T–2] ⇒ C→II (D) Acceleration due to gravity =[g]=[LT–2] ⇒ D→I

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