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PHXI08:GRAVITATION

359762 If the time period of a satellite is $20$ hours and is in equatorial plane rotating in the direction of earth's rotation ( $i . e .$ west to east), then for an observer at a fixed point on the Earth, the time interval between two consecutive overhead appearances will be

1

90 h

2

150 h

3

120 h

4

190 h

Explanation:

$T = \frac{2 π}{ω_{s} - ω_{e}} = \frac{2 π}{\frac{2 π}{T_{s}} - \frac{2 π}{T_{e}}}$
$= \frac{T_{s} T_{e}}{T_{e} - T_{s}} = \frac{20 \times 24}{24 - 20}$
$∴ T = 120 h$

PHXI08:GRAVITATION

359763 A satellite of mass $m$ revolves around the earth of radius $R$ at a height $x$ from its surface. If $g$ is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is

1

g x

2

{(\frac{g R^{2}}{R + x})}^{1 / 2}

3

\frac{g R^{2}}{R + x}

4

\frac{g R}{R - x}

Explanation:

$V = \sqrt{\frac{G M}{r}}$
$V = \sqrt{\frac{g R^{2}}{r}} = \sqrt{\frac{g R^{2}}{R + x}} = {(\frac{g R^{2}}{R + x})}^{1 / 2}$

PHXI08:GRAVITATION

359764 Assertion :
For a satellite revolving very near to earth's surface the time period of revolution is given by 1 hour 24 minutes.
Reason :
The period of revolution of a satellite depend only upon its height above the earth's surface.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

$T = 2 π \sqrt{\frac{R^{3}}{G M}}$ , the period of revolution of a satellite depends primarily on its distance $R$ from the center of the Earth. So correct option is (1)

PHXI08:GRAVITATION

359765 Two satellites of mass $m$ and 9 $m$ are orbiting a planet in orbits of radius $R$ . Their periods of revolution will be in the ratio of

1

9 : 1

2

3 : 1

3

1 : 1

4

1 : 3

KCET - 2011

PHXI08:GRAVITATION

359762 If the time period of a satellite is $20$ hours and is in equatorial plane rotating in the direction of earth's rotation ( $i . e .$ west to east), then for an observer at a fixed point on the Earth, the time interval between two consecutive overhead appearances will be

1

90 h

2

150 h

3

120 h

4

190 h

Explanation:

$T = \frac{2 π}{ω_{s} - ω_{e}} = \frac{2 π}{\frac{2 π}{T_{s}} - \frac{2 π}{T_{e}}}$
$= \frac{T_{s} T_{e}}{T_{e} - T_{s}} = \frac{20 \times 24}{24 - 20}$
$∴ T = 120 h$

PHXI08:GRAVITATION

359763 A satellite of mass $m$ revolves around the earth of radius $R$ at a height $x$ from its surface. If $g$ is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is

1

g x

2

{(\frac{g R^{2}}{R + x})}^{1 / 2}

3

\frac{g R^{2}}{R + x}

4

\frac{g R}{R - x}

Explanation:

$V = \sqrt{\frac{G M}{r}}$
$V = \sqrt{\frac{g R^{2}}{r}} = \sqrt{\frac{g R^{2}}{R + x}} = {(\frac{g R^{2}}{R + x})}^{1 / 2}$

PHXI08:GRAVITATION

359764 Assertion :
For a satellite revolving very near to earth's surface the time period of revolution is given by 1 hour 24 minutes.
Reason :
The period of revolution of a satellite depend only upon its height above the earth's surface.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

$T = 2 π \sqrt{\frac{R^{3}}{G M}}$ , the period of revolution of a satellite depends primarily on its distance $R$ from the center of the Earth. So correct option is (1)

PHXI08:GRAVITATION

359765 Two satellites of mass $m$ and 9 $m$ are orbiting a planet in orbits of radius $R$ . Their periods of revolution will be in the ratio of

1

9 : 1

2

3 : 1

3

1 : 1

4

1 : 3

KCET - 2011

PHXI08:GRAVITATION

359762 If the time period of a satellite is $20$ hours and is in equatorial plane rotating in the direction of earth's rotation ( $i . e .$ west to east), then for an observer at a fixed point on the Earth, the time interval between two consecutive overhead appearances will be

1

90 h

2

150 h

3

120 h

4

190 h

Explanation:

$T = \frac{2 π}{ω_{s} - ω_{e}} = \frac{2 π}{\frac{2 π}{T_{s}} - \frac{2 π}{T_{e}}}$
$= \frac{T_{s} T_{e}}{T_{e} - T_{s}} = \frac{20 \times 24}{24 - 20}$
$∴ T = 120 h$

PHXI08:GRAVITATION

359763 A satellite of mass $m$ revolves around the earth of radius $R$ at a height $x$ from its surface. If $g$ is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is

1

g x

2

{(\frac{g R^{2}}{R + x})}^{1 / 2}

3

\frac{g R^{2}}{R + x}

4

\frac{g R}{R - x}

Explanation:

$V = \sqrt{\frac{G M}{r}}$
$V = \sqrt{\frac{g R^{2}}{r}} = \sqrt{\frac{g R^{2}}{R + x}} = {(\frac{g R^{2}}{R + x})}^{1 / 2}$

PHXI08:GRAVITATION

359764 Assertion :
For a satellite revolving very near to earth's surface the time period of revolution is given by 1 hour 24 minutes.
Reason :
The period of revolution of a satellite depend only upon its height above the earth's surface.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

$T = 2 π \sqrt{\frac{R^{3}}{G M}}$ , the period of revolution of a satellite depends primarily on its distance $R$ from the center of the Earth. So correct option is (1)

PHXI08:GRAVITATION

359765 Two satellites of mass $m$ and 9 $m$ are orbiting a planet in orbits of radius $R$ . Their periods of revolution will be in the ratio of

1

9 : 1

2

3 : 1

3

1 : 1

4

1 : 3

KCET - 2011

PHXI08:GRAVITATION

359762 If the time period of a satellite is $20$ hours and is in equatorial plane rotating in the direction of earth's rotation ( $i . e .$ west to east), then for an observer at a fixed point on the Earth, the time interval between two consecutive overhead appearances will be

1

90 h

2

150 h

3

120 h

4

190 h

Explanation:

$T = \frac{2 π}{ω_{s} - ω_{e}} = \frac{2 π}{\frac{2 π}{T_{s}} - \frac{2 π}{T_{e}}}$
$= \frac{T_{s} T_{e}}{T_{e} - T_{s}} = \frac{20 \times 24}{24 - 20}$
$∴ T = 120 h$

PHXI08:GRAVITATION

359763 A satellite of mass $m$ revolves around the earth of radius $R$ at a height $x$ from its surface. If $g$ is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is

1

g x

2

{(\frac{g R^{2}}{R + x})}^{1 / 2}

3

\frac{g R^{2}}{R + x}

4

\frac{g R}{R - x}

Explanation:

$V = \sqrt{\frac{G M}{r}}$
$V = \sqrt{\frac{g R^{2}}{r}} = \sqrt{\frac{g R^{2}}{R + x}} = {(\frac{g R^{2}}{R + x})}^{1 / 2}$

PHXI08:GRAVITATION

359764 Assertion :
For a satellite revolving very near to earth's surface the time period of revolution is given by 1 hour 24 minutes.
Reason :
The period of revolution of a satellite depend only upon its height above the earth's surface.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

$T = 2 π \sqrt{\frac{R^{3}}{G M}}$ , the period of revolution of a satellite depends primarily on its distance $R$ from the center of the Earth. So correct option is (1)

PHXI08:GRAVITATION

359765 Two satellites of mass $m$ and 9 $m$ are orbiting a planet in orbits of radius $R$ . Their periods of revolution will be in the ratio of

1

9 : 1

2

3 : 1

3

1 : 1

4

1 : 3

KCET - 2011

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