If the gravitational field in space is given as Taking the reference point to be at cm with gravitational potential find the gravitational potential at = 3 cm in SI unit. (Given that K = 6 J cm/kg) [2023]

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Solution

Q.
If the gravitational field in space is given as $(- \frac{K}{r^{2}})$ Taking the reference point to be at $r = 2$ cm with gravitational potential $V = 10 J/kg,$ find the gravitational potential at $r$ = 3 cm in SI unit. (Given that K = 6 J cm/kg) [2023]

1 9

2 11

3 12

4 10

Ans.
(2)

$- \frac{d V}{d r} = - \frac{k}{r^{2}} \Rightarrow \int_{10}^{V} d V = \int_{2}^{3} \frac{k}{r^{2}} d r$

$V - 10 = k [\frac{1}{2} - \frac{1}{3}]$

$V - 10 = \frac{k}{6} \Rightarrow V = 11 volts$

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