question_answer

Two bodies of masses 10 kg and 100 kg are separated by a distance of 2m. The gravitational potential at the mid-point on the line joining the two is

A)  \[7.3\times {{10}^{-7}}\text{J/kg}\]  

B)  \[7.3\times {{10}^{-8}}\text{J/kg}\]

C)  \[7.3\times {{10}^{-9}}\text{J/kg}\]  

D)  \[7.3\times {{10}^{-6}}\text{J/kg}\]

Correct Answer: C

Solution :

 Gravitational potential \[|V|=\frac{Gm}{r}\] So, gravitational potential at mid-point is \[V={{V}_{1}}+{{V}_{2}}\] \[=\frac{G{{m}_{1}}}{{{r}_{1}}}+\frac{G{{m}_{2}}}{{{r}_{2}}}\] \[=\frac{6.67\times {{10}^{-11}}\times 10}{1}+\frac{6.67\times {{10}^{-11}}\times 100}{1}\] \[=6.67\times {{10}^{-11}}\times 110\] \[=7.3\times {{10}^{-9}}J/kg\]