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CBSE Class 11-science Answered

the gravitational field due to a mass distribution is E = K/ x cube in the x- direction [ k is costant ] . taking the gravitional potential to be zero at infinity , ts value at a distance x is   
Asked by drbharatkaila | 07 Sep, 2018, 11:31: PM
answered-by-expert Expert Answer
For a small displacement dx' in the given gravitational field, workdone dw on unit mass is given by
 
dw = - E × dx'  =  (- K / x'3 ) × dx' ................(1)
 
potential energy at a point x is the workdone on unit mass to bring it from infinity to x.
 
hence, Potential energy = begin mathsize 12px style integral subscript V subscript infinity end subscript superscript V subscript x end superscript d V space equals space minus integral subscript infinity superscript x fraction numerator K over denominator x apostrophe cubed end fraction d x apostrophe space end style
Vx - V∞   =    Vx begin mathsize 12px style equals space K over 2 1 over x squared end style
(we used  V∞ = 0  in the above eqn )
Answered by Thiyagarajan K | 09 Sep, 2018, 07:31: PM
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