If the gravitational force between two object | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The gravitational force provides the necessary centripetal force for the particle to move in a circular orbit.For a circular orbit,the centripetal

Vedclass · Accepted Answer

$R^0$

Vedclass · Answer

(B) The gravitational force provides the necessary centripetal force for the particle to move in a circular orbit.For a circular orbit,the centripetal force is given by $F_c = \frac{mv^2}{R}$.According to the problem,the gravitational force is $F_g \propto \frac{1}{R}$,which can be written as $F_g = \frac{K}{R}$ for some constant $K$.Equating the two forces: $\frac{mv^2}{R} = \frac{K}{R}$.Canceling $R$ from both sides,we get $mv^2 = K$.Since $m$ and $K$ are constants,$v^2$ is constant,which means $v$ is constant.Therefore,$v \propto R^0$.

If the gravitational force between two objects were proportional to $\frac{1}{R}$ (and not as $\frac{1}{R^2}$) where $R$ is the separation between them,then a particle in a circular orbit under such a force would have its orbital speed $v$ proportional to

Similar Questions

What is the orbital velocity of a satellite? Derive its equation.

If $r$ represents the radius of the orbit of a satellite of mass $m$ moving around a planet of mass $M$,the velocity of the satellite is given by

The orbital speed of an artificial satellite very close to the surface of the Earth is $V_o$. What is the orbital speed of another artificial satellite at a height equal to three times the radius of the Earth (in $,V_o$)?

Two heavenly bodies $S_1$ and $S_2$,not far from each other,are seen to revolve in orbits:

Two satellites $A$ and $B$ rotate around a planet in orbits having radii $4R$ and $R$ respectively. If the speed of satellite $A$ is $3V$,then the speed of satellite $B$ is: (in $V$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module