Q. No.An artificial satellite revolves around a planet for which gravitational force \((F)\) varies with the distance \(r\) from its centre as \(F \propto r^{2}.\) If \(v_0\) is its orbital speed, then:
1.
\(v_{0} \propto r^{-1/2}\)
2.
\(v_{0} \propto r^{3/2}\)
3.
\(v_{0} \propto r^{-3/2}\)
4.
\(v_{0} \propto r\)
A comet orbits the sun in a highly elliptical orbit. The comet has a constant:
1. linear speed
2. angular speed
3. angular momentum
4. kinetic energy
Choose the correct alternative.
| 1. | Acceleration due to gravity increases with increasing altitude. |
| 2. | Acceleration due to gravity remains unchanged with increasing altitude. |
| 3. | Acceleration due to gravity increases with increasing depth (assume the earth to be a sphere of uniform density). |
| 4. | Acceleration due to gravity decreases with increasing depth (assume the earth to be a sphere of uniform density). |
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. | \(\dfrac{d_2^2v_1}{d_1}\) |
\(T\) 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. |  |
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. | \(48~\text{N}\) |
| 1. | \(v_o=v_e\) | 2. | \(v_e=\sqrt{2v_o}\) |
| 3. | \(v_e=\sqrt{2}~v_o\) | 4. | \(v_o=\sqrt{2}~v_e\) |
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. |
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. \(\frac{r}{4}~\text{from}~4m\)
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. \(1.67\times 10^{-9}(-\hat i -\hat j) ~\text{N}\)
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