If orbital velocity of a planet is given by v = G a M b R c , then what is the value of (2 a + b -3 c /3 b ) ? [where, G = gravitational constant, M= mass of planet, R= Radius of orbit]

Question

If orbital velocity of a planet is given by v = G a M b R c , then what is the value of (2 a + b -3 c /3 b ) ? [where, G = gravitational constant, M= mass of planet, R= Radius of orbit] (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

v =√( GM / R ) ⇒ a =(1/2) ; b =(1/2) ; c =-(1/2) Now, (2 a + b -3 c /3 b )=(2((1/2))+((1/2))-3(-(1/2))/3((1)2)) =2

Q. If orbital velocity of a planet is given by $v = G^{a} M^{b} R^{c}$ , then what is the value of $\frac{2 a + b - 3 c}{3 b} ?$ [where, $G =$ gravitational constant, $M =$ mass of planet, $R =$ Radius of orbit]

$v = \frac{GM}{R}$
$\Rightarrow a = \frac{1}{2}; b = \frac{1}{2}; c = - \frac{1}{2}$
Now, $\frac{2 a + b - 3 c}{3 b} = \frac{2 ( \frac{1}{2} ) + ( \frac{1}{2} ) - 3 ( - \frac{1}{2} )}{3 ( \frac{1}{2} )}$
$= 2$

Q. If orbital velocity of a planet is given by v=GaMbRc, then what is the value of 3b2a+b−3c​? [where, G= gravitational constant, M= mass of planet, R= Radius of orbit]

v=RGM​​ ⇒a=21​;b=21​;c=−21​ Now, 3b2a+b−3c​=3(21​)2(21​)+(21​)−3(−21​)​ =2

Q. If orbital velocity of a planet is given by $v = G^{a} M^{b} R^{c}$ , then what is the value of $\frac{2 a + b - 3 c}{3 b} ?$ [where, $G =$ gravitational constant, $M =$ mass of planet, $R =$ Radius of orbit]

$v = \frac{GM}{R}$
$\Rightarrow a = \frac{1}{2}; b = \frac{1}{2}; c = - \frac{1}{2}$
Now, $\frac{2 a + b - 3 c}{3 b} = \frac{2 ( \frac{1}{2} ) + ( \frac{1}{2} ) - 3 ( - \frac{1}{2} )}{3 ( \frac{1}{2} )}$
$= 2$