If the gravitational field intensity at a point is given by g=GMr2.5. Then the potential at distance r is (Take gravitational potential at infinity is zero)

V=∫E.dr =∫∞rGMr2.5 dr =2GM3[−1r1.5]∞r =−2GM3r(1.5)

If the gravitational field intensity at a point is given by g=GMr2.5. Then the potential at distance r is (Take gravitational potential at infinity is zero)

V=∫E.dr =∫∞rGMr2.5 dr =2GM3[−1r1.5]∞r =−2GM3r(1.5)

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If the gravitational field intensity at a point is given by $g = \frac{G M}{r^{2.5}}$ . Then the potential at distance $r$ is (Take gravitational potential at infinity is zero)

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$\frac{- 2 G M}{3 r^{1.5}}$

$\frac{- G M}{r^{3.5}}$

$\frac{2 G M}{3 r^{1.5}}$

$\frac{G M}{r^{3.5}}$

answer is A.

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Detailed Solution

$V = \int E . d r = \int_{\infty}^{r} \frac{G M}{r^{2.5}} d r = \frac{2 G M}{3} {[- \frac{1}{r^{1.5}}]}_{\infty}^{r} = - \frac{2 G M}{3 r^{(1.5)}}$

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If the gravitational field intensity at a point is given by g=GMr2.5. Then the potential at distance r is (Take gravitational potential at infinity is zero)

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If the gravitational field intensity at a point is given by $g = \frac{G M}{r^{2.5}}$ . Then the potential at distance $r$ is (Take gravitational potential at infinity is zero)