Q. No.Net gravitational force at the centre of a square is found to be \(F_1\) when four particles having mass \(M,2M,3M\) and \(4M\) are placed at the four corners of the square as shown in the figure and it is \(F_2\) when the positions of \(3M\) and \(4M\) are interchanged. The ratio\(\dfrac{F_1}{F_2}\) is \(\dfrac{\alpha}{\sqrt{5}} .\) The value of \(\alpha\) is:
1. \(2\)
2. \(3\)
3. \(1\)
4. \(2\sqrt{5}\)
1. \(2\)
2. \(3\)
3. \(1\)
4. \(2\sqrt{5}\)
Subtopic: Newton's Law of Gravitation |
80%
Level 1: 80%+
Please attempt this question first.
Hints
Please attempt this question first.
A small point of mass \(m\) is placed at a distance \(2~R\) from the centre \(O\) of a big uniform solid sphere of mass \(M\) and radius \(R\). The gravitational force on m due to \(M\) is \(F_1\). A spherical part of radius \(R/3\) is removed from the big sphere as shown in the figure and the gravitational force on m due to remaining part of \(M\) is found to be \(F_2\). The value of ratio \(F_1:F_2\) is
1. \(16:9\)
2. \(12:11\)
3. \(11:10\)
4. \(12:9\)
1. \(16:9\)
2. \(12:11\)
3. \(11:10\)
4. \(12:9\)
Subtopic: Newton's Law of Gravitation |
67%
Level 2: 60%+
Please attempt this question first.
Hints
Please attempt this question first.
Four identical particles of mass \(m\) each are placed at \(4\) corners of a square. The gravitational force exerted on one of the masses by other masses is \(\left[\frac{2 \sqrt{2}+1}{32}\right] \frac{Gm^2}{l^2}.\) Then, the distance of the side of the square is:
1. \(2l\)
2. \(4l\)
3. \(\dfrac{l}{2}\)
4. \(l\)
1. \(2l\)
2. \(4l\)
3. \(\dfrac{l}{2}\)
4. \(l\)
Subtopic: Newton's Law of Gravitation |
94%
Level 1: 80%+
Please attempt this question first.
Hints
Please attempt this question first.
Two identical particles each of mass m, move in circular path due to their own mutual gravitational force. Find the velocity of the particle if the radius of circular path is a
1. \(\sqrt{{{4Gm}\over{a}}}\)
2. \(\sqrt{{{Gm}\over{2a}}}\)
3. \(\sqrt{{{2Gm}\over{a}}}\)
4. \(\sqrt{{{Gm}\over{4a}}}\)
1. \(\sqrt{{{4Gm}\over{a}}}\)
2. \(\sqrt{{{Gm}\over{2a}}}\)
3. \(\sqrt{{{2Gm}\over{a}}}\)
4. \(\sqrt{{{Gm}\over{4a}}}\)
Subtopic: Newton's Law of Gravitation |
66%
Level 2: 60%+
Please attempt this question first.
Hints
Please attempt this question first.
Two point masses (mass \(m\) each) are moving in a circle of radius \(R\) under mutual gravitational attraction. What is the speed of each mass?
| 1. | \(\begin{aligned} &\sqrt{{{GM}\over{4R}}} \\& \end{aligned}\) | 2. | \(\begin{aligned} &\sqrt{{{GM}\over{2R}}} \\& \end{aligned}\) |
| 3. | \(\begin{aligned} &\sqrt{{{GM}\over{8R}}} \\& \end{aligned}\) | 4. | \(\begin{aligned} &\sqrt{{{GM}\over{R}}} \\& \end{aligned}\) |
Subtopic: Newton's Law of Gravitation |
51%
Level 3: 35%-60%
Please attempt this question first.
Hints
Please attempt this question first.
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 |
75%
Level 2: 60%+
Please attempt this question first.
Hints
Please attempt this question first.
Given below are two statements:
| Statement I: | The law of gravitation holds good for any pair of bodies in the universe. |
| Statement II: | The weight of any person becomes zero when the person is at the centre of the earth. |
| 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 |
Level 3: 35%-60%
Please attempt this question first.
Hints
Please attempt this question first.
Three identical particles \(A,\) \(B,\) and \(C\) of mass \(100~\text{kg}\) each are placed in a straight line with \(AB=BC=13~\text m.\) The gravitational force on a fourth particle \(P\) of the same mass is \(F,\) when placed at a distance of \(13~\text m\) from particle \(B\) on the perpendicular bisector of the line \(AC.\) The value of \(F\) will be approximately:
1. \(21{G}\)
2. \(100{G}\)
3. \(59{G}\)
4. \(42{G}\)
1. \(21{G}\)
2. \(100{G}\)
3. \(59{G}\)
4. \(42{G}\)
Subtopic: Newton's Law of Gravitation |
65%
Level 2: 60%+
Please attempt this question first.
Hints
Please attempt this question first.
Two identical particles of mass \(1 ~\text{kg}\) each go around a circle of radius \(R,\) under the action of their mutual gravitational attraction. The angular speed of each particle is:
1. \(\frac{1}{2}\sqrt{\frac{G}{R^3}}\)
2. \(\sqrt{\frac{G}{2R^3}}\)
3. \(\frac{1}{2R}\sqrt{\frac{1}{G}}\)
4. \(\sqrt{\frac{2G}{R^3}}\)
1. \(\frac{1}{2}\sqrt{\frac{G}{R^3}}\)
2. \(\sqrt{\frac{G}{2R^3}}\)
3. \(\frac{1}{2R}\sqrt{\frac{1}{G}}\)
4. \(\sqrt{\frac{2G}{R^3}}\)
Subtopic: Newton's Law of Gravitation |
85%
Level 1: 80%+
Please attempt this question first.
Hints
Please attempt this question first.
A solid sphere of radius \(R\) gravitationally attracts a particle placed at \(3R\) form its centre with a force \(F_1\). Now a spherical cavity of radius \(\frac{R}{2}\) is made in the sphere (as shown in figure) and the force becomes \(F_2\). The value of \(F_1:F_2\) is:
1. \(25:36\)
2. \(36:25\)
3. \(50:41\)
4. \(41:50\)
Subtopic: Newton's Law of Gravitation |
55%
Level 3: 35%-60%
Please attempt this question first.
Hints
Please attempt this question first.
© 2026 GoodEd Technologies Pvt. Ltd.