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1.

A planet moves around the Sun \(S\) in an elliptical orbit, as shown in the figure. If its distances from the Sun at points \(A\) and \(B\) are \(r_1\)​ and \(r_2\)​ respectively, what is the ratio of its linear momentum at \(A\) to that at \(B\)?

1.	\(\dfrac{r_1}{r_2}\)	2.	\(\dfrac{r_{1}^{2}}{r_{2}^{2}}\)
3.	\(\dfrac{r_2}{r_1}\)	4.	\(\dfrac{r_{2}^{2}}{r_{1}^{2}}\)

2.

Suppose the gravitational force varies inversely as the ${\mathrm{}}^{}$\(n^{th}\) power of distance then the time period of a planet in circular orbit of radius \(R\) around the sun will be proportional to:
1. \(R^{\left(\frac{n+1}{2}\right)}\)
2. \(R^{\left(\frac{n-1}{2}\right)}\)
3. \(R^n\)
4. \(R^{\left(\frac{n-2}{2}\right)}\)

3.

A body projected vertically from the earth reaches a height equal to earth’s radius before returning to the earth. The power exerted by the gravitational force:

1.	is greatest at the instant just before the body hits the earth.
2.	remains constant throughout.
3.	is greatest at the instant just after the body is projected.
4.	is greatest at the highest position of the body.

4.

If a particle is dropped from a height \(h = 3R\) from the Earth's surface, the speed with which the particle will strike the ground is:
1. \(\sqrt{3gR}\)
2. \(\sqrt{2gR}\)
3. \(\sqrt{1.5gR}\)
4. \(\sqrt{gR}\)

5.

The initial velocity \(v_i\) required to project a body vertically upwards from the surface of the earth to just reach a height of \(10R\), where \(R\) is the radius of the earth, described in terms of escape velocity \(v_e\) is:

1.	\(\sqrt{\dfrac{10}{11}}v_e\)	2.	\(\sqrt{\dfrac{11}{10}}v_e\)
3.	\(\sqrt{\dfrac{20}{11}}v_e\)	4.	\(\sqrt{\dfrac{11}{20}}v_e\)

6.

A remote sensing satellite of the earth revolves in a circular orbit at a height of \(0.25 \times10^6~\text{m}\) above the surface of the earth. If Earth’s radius is \(6.38\times10^6~\text{m}\) and \(g=9.8~\text{ms}^{-2},\) then the orbital speed of the satellite is:
1. \(7.76~\text{kms}^{-1}\)
2. \(8.56~\text{kms}^{-1}\)
3. \(9.13~\text{kms}^{-1}\)
4. \(6.67~\text{kms}^{-1}\)

7. A projectile is fired from the surface of the earth with a velocity of \(5\) m/s and angle \(\theta\) with the horizontal. Another projectile fired from another planet with a velocity of \(3\) m/s at the same angle follows a trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet (in ms^-2) is: (given,\(g = 9.8\) ms^-2)

1.	\(3.5\)	2.	\(5.9\)
3.	\(16.3\)	4.	\(110.8\)

8.

Two spherical bodies of masses \(M\) and \(5M\) and radii \(R\) and \(2R\) are released in free space with initial separation between their centres equal to \(12R.\) If they attract each other due to gravitational force only, then the distance covered by the smaller body before the collision is:

1.	\(2.5R\)	2.	\(4.5R\)
3.	\(7.5R\)	4.	\(1.5R\)

9.

The potential energy of a satellite having mass \(m\) and rotating at a height of \(6.4\times 10^{6}~\text{m}\) from the Earth's surface is:
1. \(-0.5mg R_e\)
2. \(-mg R_e\)
3. \(-2mg R_e\)
4. \(4mg R_e\)

10.

Magnitude of potential energy (\(U\)) and time period \((T)\) of a satellite are related to each other as:
1. \(T^2\propto \frac{1}{U^{3}}\)
2. \(T\propto \frac{1}{U^{3}}\)
3. \(T^2\propto U^3\)
4. \(T^2\propto \frac{1}{U^{2}}\)