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 |
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​Let the speed of the planet at the perihelion $$P$$ in the figure shown below be $$v_p$$ and the Sun-planet distance $$SP$$ be $$r_p$$. Will the planet take equal time to traverse $$BAC$$ and $$CPB?$$

 1 no 2 yes 3 depends on the mass of the planet 4 we can't say anything

Subtopic:  Kepler's Laws |
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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 |
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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 if the mass at the vertex A is doubled? Take AG = BG = CG = 1 m.

1.

2.

3.   0

4.

Subtopic:  Newton's Law of Gravitation |
50%
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The potential energy of a system of four particles placed at the vertices of a square of side l (as shown in the figure below) and the potential at the centre of the square, respectively, are:

1.   $-5.41\frac{{\mathrm{Gm}}^{2}}{\mathrm{l}}$ and 0

2.   0 and $-5.41\frac{{\mathrm{Gm}}^{2}}{\mathrm{l}}$

3.   $-5.41\frac{{\mathrm{Gm}}^{2}}{\mathrm{l}}$ and $-4\sqrt{2}\frac{\mathrm{Gm}}{\mathrm{l}}$

4.   0 and 0

Subtopic:  Gravitational Potential Energy |
58%
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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. $$\left(\frac{3 {GM}}{5 {R}}\right)^{1 / 2}$$
2. $$\left(\frac{2 {GM}}{5 {R}}\right)^{1 / 2}$$
3. $$\left(\frac{3 {GM}}{2 {R}}\right)^{1 / 2}$$
4. $$\left(\frac{5 {GM}}{3 {R}}\right)^{1 / 2}$$

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 $9.4×{10}^{3}$ km. The mass of mars is:
1.
2.
3.
4.

Subtopic:  Satellite |
From NCERT
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You are given the following data: g 9.81 $\mathrm{m}/{\mathrm{s}}^{2}$,  m, the distance to the moon, R = $3.84×{10}^{8}$ m and the time period of the moon’s revolution is 27.3 days. Mass of the Earth ${\mathrm{M}}_{\mathrm{E}}$ in two different ways is:

1.

2.

3.

4.

Subtopic:  Satellite |
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Constant in days and kilometres is?

1.

2.

3.

4.

Subtopic:  Satellite |
57%
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The moon is at a distance of $$3.84\times10^5~\text{km}$$ from the earth. Its time period of revolution in days is: $$(\text{Given }k=\frac{4\pi^2}{GM_E}=1.33\times10^{-14}~\text{days}^{2}-\text{km}^{-3})$$
1. $$17.3$$ days
2. $$33.7$$ days
3. $$27.3$$ days
4. $$4$$ days
Subtopic:  Satellite |
63%
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