Q. No.Given below are two statements:
| Statement I: | The gravitational force acting on a particle depends on the electric charge of the particle. |
| Statement II: | The gravitational force on an extended body can be calculated by assuming the body to be a particle 'concentrated' at its centre of mass and applying Newton's law of gravitation. |
| 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: Â Newton's Law of Gravitation |
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Three stars of identical masses \(m\) move around a central star of mass \(M\) in an orbit of radius \(r.\) The net gravitational force acting on any one of the orbiting stars equals:
| 1. | \(\dfrac{GMm}{r^2}+\dfrac{2Gm^2}{r^2}\) |
| 2. | \(\dfrac{GMm}{r^2}+\dfrac{\sqrt3Gm^2}{r^2}\) |
| 3. | \(\dfrac{GMm}{r^2}+\dfrac{Gm^2}{\sqrt3r^2}\) |
| 4. | \(\dfrac{GMm}{r^2}+\dfrac{2Gm^2}{\sqrt3r^2}\) |
Subtopic: Â Newton's Law of Gravitation |
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Two particles of masses \(m_1,~m_2\) are placed on the axis of a uniform circular ring of mass \(M\) and radius \(R,\) on opposite sides of the centre of the ring. The distances of \(m_1,~m_2\) from the centre of the ring are \(x_1,~x_2\) respectively, and \(x_1~ x_2 \ll R.\) The net force on the ring vanishes. Then,
| 1. | \(\dfrac{m_{1}}{x_{1}}=\dfrac{m_{2}}{x_{2}} \) | 2. | \(\dfrac{m_{1}}{x_{1}^{2}}=\dfrac{m_{2}}{x_{2}^{2}} \) |
| 3. | \(\dfrac{m_{1}}{x_{1}^{3}}=\dfrac{m_{2}}{x_{2}^{3}} \) | 4. | \(m_{1} x_{1}=m_{2} x_{2} \) |
Subtopic: Â Newton's Law of Gravitation |
 52%
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Assume that the earth and the sun are spherical bodies with uniform mass distributions. If the radius of the sun is halved without changing its mass, the force of gravitation on the earth, exerted by the sun, will:
| 1. | be doubled |
| 2. | be \(4\) times (quadrupled) |
| 3. | be halved |
| 4. | remain unchanged |
Subtopic: Â Newton's Law of Gravitation |
 52%
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A particle of mass \(m\) is placed at the mid-point of the radius of a thin uniform spherical shell of mass \(M,\) as shown in the figure. Consider the plane that slices the shell into two parts: the plane is perpendicular to the radius and passes through \(m.\) The upper part of the shell has a mass \(\dfrac M4\) and the lower part \(\dfrac{3M}{4}.\) Let the gravitational force exerted by the upper part of the shell on the particle be \(F.\) The force exerted by the lower part of the shell on the particle is:
| 1. | \(3F\) | 2. | \(2F\) |
| 3. | \(4F\) | 4. | \(F\) |
Subtopic: Â Newton's Law of Gravitation |
 55%
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If the gravitational constant \(G\) were twice as large, the time period of the earth's orbital motion (i.e., \(1\) year) would be: (other parameters remaining the same)
| 1. | the same |
| 2. | halved |
| 3. | \(\Large\frac{1}{\sqrt2}\) times the present value |
| 4. | \({\sqrt2}\) times the present value |
Subtopic: Â Newton's Law of Gravitation |
 61%
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Given below are two statements:
| Statement I: | The gravitational force exerted by the Sun on the Earth is reduced when the Moon is between the Earth and the Sun. |
| Statement II: | The gravitational force exerted by the Sun on the Earth is reduced when the Moon is opposite to the Sun, relative to 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: Â Newton's Law of Gravitation |
 72%
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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: Â Newton's Law of Gravitation |
 76%
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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: Â Newton's Law of Gravitation |
 76%
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The force of gravitation between a particle \(A,\) and another particle \(B\) when separated by a distance \(r\) is \(F_{AB};\) while the force between a particle \(C\) and \(A\) separated by the same distance is \(4F_{AB}.\) The ratio of the masses of \(B\) and \(C\) is:
| 1. | \(4\) | 2. | \(2\) |
| 3. | \(\dfrac12\) | 4. | \(\dfrac14\) |
Subtopic: Â Newton's Law of Gravitation |
 80%
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