Two satellites of mass $m$ and $2 m$ are revolving in two circular orbits of radii $r$ and $2 r$ around an imaginary planet, on the surface of with gravitational force is inversely proportional to distance from its centre. The ratio of orbital speed of satellite is :

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Answer 1

from the figure, centripetal force,

$f = \frac{m v ^{2}}{r}$

$v^{2} = \frac{f r}{m}$

The orbital speed of 1st satellite is

$v_{1} = \frac{f r}{m}$ . . . .(1)

The orbital speed of 2nd satellite,

$v_{2} = \frac{f 2 r}{2 m}$

$v_{2} = \frac{f r}{m}$ . . . . .(2)

Ratio $v_{1} : v_{2} = 1 : 1$

The correct option is A.

Answer 2

from the figure, centripetal force,

f = \frac{m v ^{2}}{r}

v^{2} = \frac{f r}{m}

The orbital speed of 1st satellite is

v_{1} = \frac{f r}{m}

. . . .(1)

The orbital speed of 2nd satellite,

v_{2} = \frac{f 2 r}{2 m}

v_{2} = \frac{f r}{m}

. . . . .(2)

Ratio

v_{1} : v_{2} = 1 : 1

The correct option is A.

Two satellites of mass $m$ and $2 m$ are revolving in two circular orbits of radii $r$ and $2 r$ around an imaginary planet, on the surface of with gravitational force is inversely proportional to distance from its centre. The ratio of orbital speed of satellite is :

$1 : 1$

$1 : 2$

$2 : 1$

$1 : 2$

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Two satellites of mass m and 2m are revolving in two circular orbits of radii r and 2r around an imaginary planet, on the surface of with gravitational force is inversely proportional to distance from its centre. The ratio of orbital speed of satellite is :

1:1

1:2

2:1

1:2​

from the figure, centripetal force, f=rmv2​ v2=mfr​ The orbital speed of 1st satellite is v1​=mfr​​. . . .(1) The orbital speed of 2nd satellite, v2​=2mf2r​​ v2​=mfr​​. . . . .(2) Ratio v1​:v2​=1:1 The correct option is A.

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Two satellites of mass $m$ and $2 m$ are revolving in two circular orbits of radii $r$ and $2 r$ around an imaginary planet, on the surface of with gravitational force is inversely proportional to distance from its centre. The ratio of orbital speed of satellite is :

$1 : 1$

$1 : 2$

$2 : 1$

$1 : 2$

A satellite of earth is revolving in a circular orbit with uniform velocity $v$ . If gravitational force suddenly disappears, the satellite will:

Two satellites of masses $m_{1}$ and $m_{2}$ ( $m_{1}$ > $m_{2}$ ) are revolving round the earth in circular orbits of radii $r_{1}$ and $r_{2}$ ( $r_{1}$ > $r_{2}$ ) respectively. Which of the following statements is true regarding their speeds $v_{1}$ and $v_{2}$ $v_{1}$ ?

Suppose the gravitational force varies inversely as the $n^{t h}$ power of distance then the time period $T$ of a satellite revolving in a circular orbit of radius $r$ around the earth is proportional to