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Q7.21: NCERT Physics - Part 1 GRAVITATION 7.21 Solution: Two heavy spheres each of mass 100 kg and radius 0.10 m are…

Two heavy spheres each of mass 100 kg and radius 0.10 m are placed 1.0 m apart on a horizontal table. What is the gravitational force and potential at the mid point of the line joining the centres of the spheres? Is an object placed at that point in equilibrium? If so, is the equilibrium stable or unstable?

Step-by-Step Verified Solution

**Answer:** Force = 0; Potential = −2.7×10−8-2.7 \times 10^{-8} J/kg; Yes; Unstable. **Step-by-Step Explanation:** At the midpoint, the gravitational forces from the two spheres are equal and opposite, so net force = 0. Gravitational potential:
V=−GMr−GMr=−2GMr=−2(6.67×10−11)(100)0.5=−2.7×10−8 J/kgV = -\frac{GM}{r} - \frac{GM}{r} = -\frac{2GM}{r} = -\frac{2(6.67 \times 10^{-11})(100)}{0.5} = -2.7 \times 10^{-8} \text{ J/kg}
An object placed at this point is in equilibrium. The equilibrium is unstable because any small displacement will result in a net force pushing the object further away from the midpoint [citation:5].

All Questions in this Chapter

Q7.1 Q7.2 Q7.3 Q7.4 Q7.5 Q7.6 Q7.7 Q7.8 Q7.9 Q7.10 Q7.11 Q7.12 Q7.13 Q7.14 Q7.15 Q7.16 Q7.17 Q7.18 Q7.19 Q7.20 Q7.21

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