Match List - I with List - II:

  List - I   List - II
(a) Gravitational constant (G) (i) [L2T-2]
(b) Gravitational potential energy (ii) [M-1L3T-2]
(c) Gravitational potential (iii) [LT-2]
(d) Gravitational intensity (iv) [ML2T-2]

Choose the correct answer from the options given below:

  1. (a) - (iv), (b) - (ii), (c) - (i), (d) - (iii)
  2. (a) - (ii), (b) - (i), (c) - (iv), (d) - (iii)
  3. (a) - (ii), (b) - (iv), (c) - (i), (d) - (iii)
  4. (a) - (ii), (b) - (iv), (c) - (iii), (d) - (i)

Answer (Detailed Solution Below)

Option 3 : (a) - (ii), (b) - (iv), (c) - (i), (d) - (iii)
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Detailed Solution

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Concept: 

(a) gravitational constant is = G = Fr2/Mm

we know F = GMm/r2 =>  G = Fr2/Mm where F = ma = M1L1T-2 

so G = M-1L3T-2  so (a) matches with (ii)

(b) Gravitational potential energy = mass × altitude × acceleration due to gravity

dimensional formula of mass = [M1 L0 T0]   and dimensional formula of altitude = [M0 L1 T0]

and acceleration due to gravity (g) = [M0 L1 T-2]

then dimensions of Gravitational potential energy = [M1 L2 T-2] so that it matches with (iv).

(c) gravitational potential (V) = work done/ mass 

dimensional formula of work done = Force× distance = [M1 L2 T-2 

then dimensions of Gravitational potential = [M0 L2 T-2] so that it matches with (i).

(d)  Gravitational Intensity (Eg) = [- GM/r2]  

from above gravitational constant has a dimensional formula as G = M-1L3T-2 

then, dimensions of Gravitational intensity = [M0 L1 T-2] so that it matches with (iii).

Explanation:

As we have concluded in the concept section :

(a) matches with (ii)

(b) matches with (iv).

(c) matches with (i).

(d)matches with (iii).

Hence option 3) is correct.

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