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A mass \(M\) is split into two parts, \(m\) and \((M–m),\) which are then separated by a certain distance. What ratio of \(m/M\) maximizes the gravitational force between the two parts?

1. \(1/3\)                           

2. \(1/2\)

3. \(1/4\)                           

4. \(1/5\)

Subtopic:  Newton's Law of Gravitation |
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The figure shows two concentric shells of masses \(m,~\) and \(m.~\) At which point a particle of mass \(m\) shall experience zero gravitational force because of them?

                      

1. \(A\)

2. \(C\)

3. \(D\)

4. \(B\)

Subtopic:  Newton's Law of Gravitation |
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Two objects of equal masses placed at certain distance from each other attracts each other with a force of \(F\). If one-third mass of one object is transferred to the other object, then the new force will be:
1. \( \dfrac{2}{9}{F} \) 2. \(\dfrac{16}{9} F\)
3. \(\dfrac{8}{9} F\) 4. \(F\)
Subtopic:  Newton's Law of Gravitation |
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The gravitational force between two objects:
1. occurs only when the objects have very different masses
2. is greater on the more massive of the two objects
3. is not an attractive force
4. increases in magnitude as the two objects approach each other
Subtopic:  Newton's Law of Gravitation |
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Level 2: 60%+
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Three identical particles, each of mass \(m,\) are kept at the three vertices of an equilateral triangle of side \(a.\) The physical quantities, associated with the gravitational field of these particles, are given under Column-I, while their values are in Column-II. Match them.

Column-I Column-II
\(\mathrm{(A)}\) Force on any particle
(units of \(Gm^2/a^2\))
\(\mathrm{(I)}\) \(3\)
\(\mathrm{(B)}\) Potential energy of the system
(units of \(-Gm^2/a\))
\(\mathrm{(II)}\) \(\sqrt3\)
\(\mathrm{(C)}\) Gravitational potential due to any particle at the centre \((O)\)
(units of \(-Gm/a\))
\(\mathrm{(III)}\) \(\dfrac43\)
\(\mathrm{(D)}\) Gravitational field at the mid-point of a side
(units of \(Gm/a^2\))
\(\mathrm{(IV)}\) \(\dfrac23\)
 
1. \(\mathrm{A-I, B-II, C-IV, D-III}\)
2. \(\mathrm{A-III, B-I, C-I, D-II}\)
3. \(\mathrm{A-II, B-I, C-II, D-III}\)
4. \(\mathrm{A-I, B-III, C-IV, D-II}\)
Subtopic:  Newton's Law of Gravitation |
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The net gravitational force acting on a particle, when three such identical particles (mass \(m,\) each) are situated on the three vertices of an equilateral triangle of side \(a,\) is:
1. \({\dfrac{2Gm^2}{a^2}}\) 2. \({\dfrac{Gm^2}{a^2}}\)
3. \({\dfrac{\sqrt3}{2}\dfrac{Gm^2}{a^2}}\) 4. \({\dfrac{\sqrt3Gm^2}{a^2}}\)
Subtopic:  Newton's Law of Gravitation |
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Given below are two statements:
Statement I: The force of gravitation between two particles acts on the respective particles only when there is no other medium between them.
Statement II: The gravitational force between two uniform spheres is inversely proportional to the square of the distance between their centres.
 
1. Statement I is incorrect and Statement II is correct.
2. Both Statement I and Statement II are correct.
3. Both Statement I and Statement II are incorrect.
4. Statement I is correct and Statement II is incorrect.
Subtopic:  Newton's Law of Gravitation |
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