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What is the minimum energy required to l...

What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R?

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From the law of conservation of energy `(-GMm)/R+KE_("imparted")=(-GMm)/(2xx3R)`
`KE_("imparted")=(GMm)/R(1-1/6)=5/6((GMm)/R)`
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NARAYNA-GRAVITATION-EXERCISE -IV
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  2. The earth is an approximate sphere. If the interior contained matter w...

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  3. Different points in the earth are at slightly different distance from ...

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  4. Satellites orbiting the earth have finite life and sometimes debris of...

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  5. Particles of masses 2M, m and M are respectively at points A, B and C ...

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  6. A point mass is orbiting a significant mass M lying at the focus of th...

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  7. A planet of mass m revolves in elliptical orbit around the sun of mass...

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  8. A planet revolves around the sun in elliptical orbit of eccentricity '...

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  9. The gravitational field in a region is given by vecE = (3hati- 4hatj) ...

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  10. A solid sphere of uniform density and mas M has radius 4M. Its centre ...

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  11. A point P lies on the axis of a fixed ring of mass M and radius R, at ...

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  12. Two having masses M and 2M, respectively, having the same radius R are...

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  13. A point of mass m is released from rest at a distance of 3R from the c...

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  14. A small body of superdense material, whose mass is twice the mass of t...

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  15. From a solid sphere of mass m and radius R, a spherical portion of rai...

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  16. The density of the core of a planet is rho(1) and that of the outer sh...

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  17. Two concnetric shells of different masses m(1) and m(2) are having a ...

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  18. Suppose a vertical tunnel is dug along the diameter of earth assumed t...

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  19. The centres of a ring of mass m and a sphere of mass M of equal radius...

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  20. A mass m extends a vertical helical spring of spring constant k by xm ...

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  21. A spherical shell is cut into two pieces along a chord as shown in the...

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