If the gravitational field in the space is given as (-K/r²). 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) (a) 9 (b) 11 (c) 10 (d) 12

Answer: (b). dV/dr = -E = K/r² ⇒ V(r) = -K/r + C At r = 2 cm: 10 = -6/2 + C ⇒ C = 13 At r = 3 cm: V = -6/3 + 13 = 11 J/kg So the answer is (b) 11.

If the gravitational field in the space is given as (-K/r²). Taking… | JEE Main 2023 (30 Jan, Shift 1)

Q11JEE Main 2023 · 30 JAN · SHIFT 1Medium

Gravitational Potential & Energy

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

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Answer: (b)

$\frac{dV}{dr} = -E = \frac{K}{r^2} \Rightarrow V(r) = -\frac{K}{r} + C$
At $r = 2$ cm: $10 = -\frac{6}{2} + C \Rightarrow C = 13$
At $r = 3$ cm: $V = -\frac{6}{3} + 13 = 11\ \text{J/kg}$
So the answer is (b) 11.

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