# If $$v_e$$ is the escape velocity and $$v_0$$ is the orbital velocity of a satellite for orbit close to the earth's surface, then these  are related by: 1. $$v_o=v_e$$ 2. $$v_e=\sqrt{2v_o}$$ 3. $$v_e=\sqrt{2}~v_o$$ 4. $$v_o=\sqrt{2}~v_e$$

Subtopic:  Orbital velocity |
76%
From NCERT
AIPMT - 2012
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For a satellite moving in an orbit around the earth, the ratio of kinetic energy to potential energy is:
1. $\frac{1}{\sqrt{2}}$
2. $$2$$
3. $\sqrt{2}$
4. $\frac{1}{2}$

Subtopic:  Satellite |
81%
From NCERT
AIPMT - 2005
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Two spheres of masses $$m$$ and $$M$$ are situated in air and the gravitational force between them is $$F.$$ If the space around the masses is filled with a liquid of specific density $$3,$$ the gravitational force will become:
1. $$3F$$
2. $$F$$
3. $$F/3$$
4. $$F/9$$

Subtopic:  Newton's Law of Gravitation |
82%
From NCERT
AIPMT - 2003
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Let the speed of the planet at the perihelion $$P$$ in figure shown below be $$v_{_P}$$ and the Sun-planet distance $$\mathrm{SP}$$ be $$r_{_P}.$$ Relation between $$(r_{_P},~v_{_P})$$ to the corresponding quantities at the aphelion $$(r_{_A},~v_{_A})$$ is:

 1 $$v_{_P} r_{_P} =v_{_A} r_{_A}$$ 2 $$v_{_A} r_{_P} =v_{_P} r_{_A}$$ 3 $$v_{_A} v_{_P} = r_{_A}r_{_P}$$ 4 none of these
Subtopic:  Kepler's Laws |
78%
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Three equal masses of $$m$$ kg each are fixed at the vertices of an equilateral triangle $$ABC.$$ What is the force acting on a mass $$2m$$ placed at the centroid $$G$$ of the triangle
(
Take $$AG=BG=CG=1$$ m.)

1. $$Gm^2(\hat{i}+\hat{j})$$
2. $$Gm^2(\hat{i}-\hat{j})$$
3. zero
4. $$2Gm^2(\hat{i}+\hat{j})$$

Subtopic:  Newton's Law of Gravitation |
82%
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Two uniform solid spheres of equal radii $${R},$$ but mass $${M}$$ and $$4M$$ have a centre to centre separation $$6R,$$ as shown in the figure. The two spheres are held fixed. A projectile of mass $$m$$ is projected from the surface of the sphere of mass $$M$$ directly towards the centre of the second sphere. The expression for the minimum speed $$v$$ of the projectile so that it reaches the surface of the second sphere is:

1. $$\left(\dfrac{3 {GM}}{5 {R}}\right)^{1 / 2}$$
2. $$\left(\dfrac{2 {GM}}{5 {R}}\right)^{1 / 2}$$
3. $$\left(\dfrac{3 {GM}}{2 {R}}\right)^{1 / 2}$$
4. $$\left(\dfrac{5 {GM}}{3 {R}}\right)^{1 / 2}$$
Subtopic:  Gravitational Potential Energy |
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The planet Mars has two moons, Phobos and Delmos. Phobos has a period of $$7$$ hours, $$39$$ minutes and an orbital radius of $$9 . 4 \times 10^{3}$$ km. The mass of mars is:
 1 $$6 . 48 \times 10^{23} \text{ kg}$$ 2 $$6 . 48 \times 10^{25} \text{ kg}$$ 3 $$6 . 48 \times 10^{20} \text{ kg}$$ 4 $$6 . 48 \times 10^{21} \text{ kg}$$
Subtopic:  Satellite |
From NCERT
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The time period of an earth satellite in circular orbit is independent of:

 1 the mass of the satellite 2 radius of the orbit 3 none of them 4 both of them
Subtopic:  Satellite |
78%
From NCERT
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Two satellites A and B move around the earth in the same orbit. The mass of B is twice the mass of A. Then:

 1 speeds of A and B are equal. 2 the potential energy of earth $$+$$ A is same as that of earth $$+$$ B. 3 the kinetic energy of A and B are equal. 4 the total energy of earth $$+$$ A is same as that of earth $$+$$ B.

Subtopic:  Satellite |
68%
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Which of the following quantities remain constant in a planetary motion (consider elliptical orbits) as seen from the sun?
1. speed
2. angular speed
3. kinetic energy
4. angular momentum

Subtopic:  Kepler's Laws |
84%
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