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. \(2\sqrt{5}\)
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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. \(12:9\)
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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. \(l\)
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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. \(\sqrt{{{Gm}\over{4a}}}\)
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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. | \(\begin{aligned} &\sqrt{{{GM}\over{R}}} \\& \end{aligned}\) |
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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. | \(F\) |
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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. |
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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. \(42{G}\)
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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. \(\sqrt{\frac{2G}{R^3}}\)
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Four particles each of mass \(M,\) move along a circle of radius \(R\) under the action of their mutual gravitational attraction as shown in the figure. The speed of each particle is:
1. \(\frac{1}{2} \sqrt{\frac{G M}{R(2 \sqrt{2}+1)}}\)
2. \(\frac{1}{2} \sqrt{\frac{{GM}}{{R}}(2 \sqrt{2}-1)}\)
3. \(\frac{1}{2} \sqrt{\frac{G M}{R}(2 \sqrt{2}+1)}\)
4. \(\sqrt{\frac{{GM}}{{R}}}\)
1. \(\frac{1}{2} \sqrt{\frac{G M}{R(2 \sqrt{2}+1)}}\)
2. \(\frac{1}{2} \sqrt{\frac{{GM}}{{R}}(2 \sqrt{2}-1)}\)
3. \(\frac{1}{2} \sqrt{\frac{G M}{R}(2 \sqrt{2}+1)}\)
4. \(\sqrt{\frac{{GM}}{{R}}}\)
Subtopic: Newton's Law of Gravitation |
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