Question

If the gravitational force between two objects were proportional to 1/R; where R is separation between them, then a particle in circular orbit under such a force would have its orbital speed v proportional to

• A. $1 / R ^ { 2 }$
• B. $R ^ { 0 }$
• C. $R ^ { 1 }$
• D. $1 / R$

Answer 1

Answer: (B)

$R ^ { 0 }$

Answer 2

If $v \propto \frac { 1 } { \sqrt { R ^ { n - 1 } } }$; here $n = 1$ $\therefore v \propto \frac { 1 } { \sqrt { R ^ { 1 - 1 } } } \propto R ^ { 0 }$.