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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 |
Level 4: Below 35%
Hints
Two stars of equal mass rotate about a common centre-of-mass in a common circular orbit of radius \(R.\) The total mass of the stars is \(M.\)
The gravitational force exerted by the stars, on each other, is:
The gravitational force exerted by the stars, on each other, is:
| 1. | \(\Large\frac{GM^2}{4R^2}\) | 2. | \(\Large\frac{GM^2}{R^2}\) |
| 3. | \(\Large\frac{GM^2}{16R^2}\) | 4. | \(\Large\frac{4GM^2}{R^2}\) |
Subtopic: Â Newton's Law of Gravitation |
Level 3: 35%-60%
Please attempt this question first.
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Please attempt this question first.
Two identical-mass planets (mass: \(m\)) move around a Star (mass: \(M\)) in a circular orbit of radius \(r,\) in a symmetrical manner. The orbital speed of the planets is:
1. \(\sqrt{\dfrac{2GM}{r}}\)
2. \(\sqrt{\dfrac{5GM}{4r}}\)
3. \(\sqrt{\dfrac{G(M+m)}{r}}\)
4. \(\sqrt{\dfrac{G[M+(m/4)]}{r}}\)
Subtopic: Â Newton's Law of Gravitation |
Level 3: 35%-60%
Please attempt this question first.
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Please attempt this question first.
Given below are two statements:
| Assertion (A): | The gravitational force of the earth on a person decreases when the sun is directly overhead. |
| Reason (R): | The gravitational force of the earth and the sun act in opposite directions on us when it is directly overhead. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | (A) is False but (R) is True. |
Subtopic: Â Newton's Law of Gravitation |
Level 3: 35%-60%
Hints
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 |
 53%
Level 3: 35%-60%
Hints
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%
Level 3: 35%-60%
Hints
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 |
 57%
Level 3: 35%-60%
Hints
The gravitational acceleration due to a uniform disc of mass \(m\) is measured at a point \((P)\) on the axis of the disc, at a distance \(x,\) from its centre. At very large distances (\(x\gg R,\) the radius of the disc), this acceleration varies as:
| 1. | \(\large\dfrac{1}{x^2}\) | 2. | \(\large\dfrac{1}{\sqrt x}\) |
| 3. | \(\large\dfrac{1}{x}\) | 4. | \(\large\dfrac{1}{x^{3/2}}\) |
Subtopic: Â Newton's Law of Gravitation |
 61%
Level 2: 60%+
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Q. No.
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