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

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(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,$v \propto R^0$.

Class 11 Physics Gravitation Motion of Satellites in Circular Orbits and Planets in Elliptical Orbits

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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

AIPMT 1994 All AIPMT

AIPMT 1989 All AIPMT

A
$\frac{1}{R^2}$
B
$R^0$
C
$R^1$
D
$\frac{1}{R}$

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Class 11

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Gravitation

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Motion of Satellites in Circular Orbits and Planets in Elliptical Orbits

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AIPMT 1994 Paper All AIPMT years →

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$A$ satellite is to revolve around the Earth in a circle of radius $8000\, km$. The speed at which this satellite must be projected into an orbit will be......... $km/s$.

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Suppose an astronaut throws a spoon out of a spacecraft. Will the spoon fall to the Earth?

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Shown are several curves [fig. $(a)$,$(b)$,$(c)$,$(d)$,$(e)$,$(f)$]. Explain with reason,which ones amongst them can be possible trajectories traced by a projectile (neglect air friction).

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Two particles of identical mass are moving in circular orbits under a potential given by $V(r) = K r^{-n}$,where $K$ is a constant. If the radii of their orbits are $r_1$ and $r_2$ and their speeds are $v_1$ and $v_2$,respectively,then:

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$A$ planet of mass $m$ moves in an elliptical orbit around an unknown star of mass $M$ such that its maximum and minimum distances from the star are equal to $r_1$ and $r_2$ respectively. The angular momentum of the planet relative to the centre of the star is

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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

$A$ satellite is to revolve around the Earth in a circle of radius $8000\, km$. The speed at which this satellite must be projected into an orbit will be......... $km/s$.

Suppose an astronaut throws a spoon out of a spacecraft. Will the spoon fall to the Earth?

Shown are several curves [fig. $(a)$,$(b)$,$(c)$,$(d)$,$(e)$,$(f)$]. Explain with reason,which ones amongst them can be possible trajectories traced by a projectile (neglect air friction).

Two particles of identical mass are moving in circular orbits under a potential given by $V(r) = K r^{-n}$,where $K$ is a constant. If the radii of their orbits are $r_1$ and $r_2$ and their speeds are $v_1$ and $v_2$,respectively,then:

$A$ planet of mass $m$ moves in an elliptical orbit around an unknown star of mass $M$ such that its maximum and minimum distances from the star are equal to $r_1$ and $r_2$ respectively. The angular momentum of the planet relative to the centre of the star is

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