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Gravitation question

2025 · 3 Apr · Shift 1 · Q56
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Gravitation question

2025 · 3 Apr · Shift 1 · Q56

JEE MainPhysicsGravitationMCQ+4 / −1

 Match the LIST-I with LIST-II \text { Match the LIST-I with LIST-II } Match the LIST-I with LIST-II 

List - I
 List - II
A.
 Gravitational constant \text { Gravitational constant } Gravitational constant 
 I.
[LT−2]\left[\mathrm{LT}^{-2}\right][LT−2]
B.
 Gravitational potential energy \text { Gravitational potential energy } Gravitational potential energy 

 II.
[L2 T−2]\left[\mathrm{L}^2 \mathrm{~T}^{-2}\right][L2 T−2]
C.
 Gravitational potential \text { Gravitational potential } Gravitational potential 

 III.

[ML2 T−2]\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right][ML2 T−2]
D.
 Acceleration due to gravity \text { Acceleration due to gravity } Acceleration due to gravity 

 IV.
[M−1 L3 T−2]\left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right][M−1 L3 T−2]
Choose the correct answer from the options given below:
  1. A
    A-IV, B-III, C-II, D-I
  2. B
    A-II, B-IV, C-III, D-I
  3. C
    A-I, B-III, C-IV, D-II
  4. D
    A-III, B-II, C-I, D-IV
View written solutionFree

Correct answer: A

  1. Find dimensions of each quantity in List-I

We match each physical quantity with its dimensional formula.

  1. A. Gravitational constant GGG

From Newton’s law of gravitation, F=Gm1m2r2F = \frac{G m_1 m_2}{r^2}F=r2Gm1​m2​​ So, G=Fr2m1m2G = \frac{F r^2}{m_1 m_2}G=m1​m2​Fr2​ Now,

  • [F]=[MLT−2][F] = [M L T^{-2}][F]=[MLT−2]
  • [r2]=[L2][r^2] = [L^2][r2]=[L2]
  • [m1m2]=[M2][m_1 m_2] = [M^2][m1​m2​]=[M2]

Therefore, [G]=[MLT−2][L2][M2]=[M−1L3T−2][G] = \frac{[M L T^{-2}] [L^2]}{[M^2]} = [M^{-1} L^3 T^{-2}][G]=[M2][MLT−2][L2]​=[M−1L3T−2] So, A →\to→ IV.

  1. B. Gravitational potential energy

Potential energy has dimensions of energy.

We know, [Energy]=[Work]=[Force]⋅[distance][\text{Energy}] = [\text{Work}] = [\text{Force}] \cdot [\text{distance}][Energy]=[Work]=[Force]⋅[distance] =[MLT−2][L]=[ML2T−2]= [M L T^{-2}] [L] = [M L^2 T^{-2}]=[MLT−2][L]=[ML2T−2] So, B →\to→ III.

  1. C. Gravitational potential

Gravitational potential is potential energy per unit mass: V=UmV = \frac{U}{m}V=mU​ Thus, [V]=[ML2T−2][M]=[L2T−2][V] = \frac{[M L^2 T^{-2}]}{[M]} = [L^2 T^{-2}][V]=[M][ML2T−2]​=[L2T−2] So, C →\to→ II.

  1. D. Acceleration due to gravity ggg

Acceleration has dimensions: [g]=[LT−2][g] = [L T^{-2}][g]=[LT−2] So, D →\to→ I.

  1. Final matching
  • A →\to→ IV
  • B →\to→ III
  • C →\to→ II
  • D →\to→ I

This corresponds to Option A.

  1. Comparison with stored answer

Stored correct answer: A

Our derived answer: A

So, the answer agrees with the stored answer.

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