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Standard IX

Physics

Simple Pendulum

A satellite i...

Question

A satellite is moving on a circular orbit around a planet. A sharp impulse is given to the satellite such that escapes from the gravitational field of the planet. The impulse can be given in two different ways ways as shown. The ratio of the impulse given in the two different cases $\frac{P_{1}}{P_{2}}$ is

1

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2

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\sqrt{2} - 1

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\sqrt{2} + 1

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Solution

The correct option is C $\sqrt{2} - 1$
As to escape gravitational field it require some extra kinetic energy so if you give impulse in any way does not matter if velocity gain by mass is same then it will escape gravitational field so ratio of impulse is 1

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Similar questions

Q. A satellite revolving around a planet has orbital velocity

10 k m / s

. The additional velocity required for the satellite to escape to from the gravitational field of the planet is:

Two satellites

A

and

B

are revolving around the earth in circular orbits of radius

r_{1}

and

r_{2}

respectively with

r_{1} < r_{2}

. Plane of motion of the two are same. At position

1

A

is given an impulse in the direction of velocity by firing a rocket so that it follows an elliptical path to meet

B

at position

2

as shown. Focal length of the elliptical path are

r_{1}

and

r_{2}

respectively. At position

2

A

is given another impulse so that velocities of

A

and

B

2

become equal and the two move together.
For any elliptical path of the satellite time period of revolution is given by Kepler's planetary law as

T^{2} \propto r^{3}

where

a

is semi major axis of the ellipse which is

\frac{r_{1} + r_{2}}{2}

in this case. Also angular momentum of any satellite revolving around the Earth will remain a constant about Earth's centre as force of gravity on the satellite which keeps it in elliptical path is along its position vector relative to the earth centre.

If the two bodies have same mass then,

The ratio of the K.E. required to be given to the satellite to escape earth's gravitational field to the K.E. required to be given so that the satellite moves in a circular orbit just above earth atmosphere is

Q. If a satellite is revolving around a planet of mass M in an elliptical orbit of semi-major axis a. Show that the orbital speed of the satellite when it is at a distance r from the planet will be given by

V^{2} = G M [\frac{2}{r} - \frac{1}{a}]

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A satellite is moving on a circular orbit around a planet. A sharp impulse is given to the satellite such that escapes from the gravitational field of the planet. The impulse can be given in two different ways ways as shown. The ratio of the impulse given in the two different cases P1P2 is

The correct option is C √2−1As to escape gravitational field it require some extra kinetic energy so if you give impulse in any way does not matter if velocity gain by mass is same then it will escape gravitational field so ratio of impulse is 1

The correct option is C $\sqrt{2} - 1$
As to escape gravitational field it require some extra kinetic energy so if you give impulse in any way does not matter if velocity gain by mass is same then it will escape gravitational field so ratio of impulse is 1