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The gravitational field due to a mass di...

The gravitational field due to a mass distribution is given by `E=-K//x^3` in x-direction. Taking the gravitational potential to be zero at infinity, find its value at a distance `x`.

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To find the gravitational potential \( V \) at a distance \( x \) from a mass distribution given the gravitational field \( E = -\frac{K}{x^3} \), we can follow these steps: ### Step 1: Understand the relationship between gravitational field and potential The relationship between the gravitational field \( E \) and the gravitational potential \( V \) is given by: \[ dV = -E \, dx \] This means that the change in potential \( dV \) is equal to the negative of the gravitational field \( E \) multiplied by the differential distance \( dx \). ...
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NARAYNA-GRAVITATION-EXERCISE -IV
  1. The gravitational field due to a mass distribution is given by E=-K//x...

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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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