Question

If orbital velocity of planet is given by $v = G ^ { a } M ^ { b } R ^ { c }$ , then

• A. $a = 1 / 3 , b = 1 / 3 , c = - 1 / 3$
• B. $a = 1 / 2 , b = 1 / 2 , c = - 1 / 2$
• C. $a = 1 / 2 , b = - 1 / 2 , c = 1 / 2$
• D. $a = 1 / 2 , b = - 1 / 2 , c = - 1 / 2$

Answer 1

Answer: (B)

$a = 1 / 2 , b = 1 / 2 , c = - 1 / 2$

Answer 2

$v = \sqrt { \frac { G M } { R } }$ $= G ^ { 1 / 2 } M ^ { 1 / 2 } R ^ { - 1 / 2 }$