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 Jcm / kg)

Solution

Physics sir · 4 steps

Potential is minus the integral of the field, so integrate -K/r² from 2 cm to 3 cm and add to 10.

1. Field to potential. The field is E = -dV/dr, so dV = -E dr. Integrate from the reference point r₀ = 2 cm out to r = 3 cm.

   V(r) - V(r₀) = -∫_(r₀)ʳ(-K/r²)dr = K(1/r₀ - 1/r)

2. Put in numbers. K is in J cm/kg and r is in cm, so K/r comes out directly in J/kg. The change is 6(1/2 - 1/3) = 6 × 1/6 = 1 J/kg.
3. Check the sign. The field points inward (attractive), so moving outward means moving against the field. The potential must rise, and it does: +1 J/kg.
4. So. V(3 cm) = 10 + 1 = 11 J/kg, which is option (b).

The idea to keep. Use dV = -E dr and integrate from the reference point. For an attractive field, potential always increases as you move outward.

Answer from the NTA final answer key. Solution by PrepWiser.