Q. No.A planet is revolving around a massive star in a circular orbit of radius \(R\). If the gravitational force of attraction between the planet and the star is inversely proportional to \(R^3,\) then the time period of revolution \(T\) is proportional to:
1. \(R^5\)
2. \(R^3\)
3. \(R^2\)
4. \(R\)
1. \(R^5\)
2. \(R^3\)
3. \(R^2\)
4. \(R\)
Three identical point masses, each of mass \(1~\text{kg}\) lie at three points \((0,0),\) \((0,0.2~\text{m}),\) \((0.2~\text{m}, 0).\) The net gravitational force on the mass at the origin is:
1. \(6.67\times 10^{-9}(\hat i +\hat j)~\text{N}\)
2. \(1.67\times 10^{-9}(\hat i +\hat j) ~\text{N}\)
3. \(1.67\times 10^{-9}(\hat i -\hat j) ~\text{N}\)
4. \(1.67\times 10^{-9}(-\hat i -\hat j) ~\text{N}\)
Two particles of mass \(m\) and \(4m\) are separated by a distance \(r.\) Their neutral point is at:
1. \(\frac{r}{2}~\text{from}~m\)
2. \(\frac{r}{3}~\text{from}~4m\)
3. \(\frac{r}{3}~\text{from}~m\)
4. \(\frac{r}{4}~\text{from}~4m\)
Given below are two statements:
| Assertion (A): | When a body is raised from the surface of the earth, its potential energy increases. |
| Reason (R): | The potential energy of a body on the surface of the earth is zero. |
| 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. | Both (A) and (R) are False. |
A particle is located midway between two point masses each of mass \(M\) kept at a separation \(2d.\) The escape speed of the particle is:
(neglecting the effect of any other gravitational effect)
1. \(\sqrt{\frac{2 GM}{d}}\)
2. \(2 \sqrt{\frac{GM}{d}}\)
3. \(\sqrt{\frac{3 GM}{d}}\)
4. \(\sqrt{\frac{GM}{2 d}}\)
1. \(-E_0\)
2. \(1.5E_0\)
3. \(2E_0\)
4. \(E_0\)
A body weighs \(72~\text{N}\) on the surface of the earth. What is the gravitational force on it at a height equal to half the radius of the earth?
| 1. | \(32~\text{N}\) | 2. | \(30~\text{N}\) |
| 3. | \(24~\text{N}\) | 4. | \(48~\text{N}\) |
\(T\) is the time period of revolution of a planet revolving around the sun in an orbit of mean radius \(R\). Identify the incorrect graph.
| 1. |  |
2. |  |
| 3. |  |
4. |  |
The law of gravitation states that the gravitational force between two bodies of mass \(m_1\) \(m_2\) is given by:
\(F=\dfrac{Gm_1m_2}{r^2}\)
\(G\) (gravitational constant) \(=7\times 10^{-11}~\text{N-m}^2\text{kg}^{-2}\)
\(r\) (distance between the two bodies) in the case of the Earth and Moon \(=4\times 10^8~\text{m}\)
\(m_1~(\text{Earth})=6\times 10^{24}~\text{kg}\)
\(m_2~(\text{Moon})=7\times 10^{22}~\text{kg}\)
What is the gravitational force between the Earth and the Moon?
1. \(1.8375 \times 10^{19}~\text{N}\)
2. \(1.8375 \times 10^{20}~\text{N}\)
3. \(1.8375 \times 10^{25}~\text{N}\)
4. \(1.8375 \times 10^{26}~\text{N}\)
A planet moves around the sun. At a point \(P,\) it is closest to the sun at a distance \(d_1\) and has speed \(v_1.\) At another point \(Q,\) when it is farthest from the sun at distance \(d_2,\) its speed will be:
| 1. | \(\dfrac{d_2v_1}{d_1}\) | 2. | \(\dfrac{d_1v_1}{d_2}\) |
| 3. | \(\dfrac{d_1^2v_1}{d_2}\) | 4. | \(\dfrac{d_2^2v_1}{d_1}\) |
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