question_answer

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

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

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

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

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

Correct Answer: C

Solution :

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