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A satellite of the earth is revolving in...

A satellite of the earth is revolving in circular orbit with a uniform velocity `V`. If the gravitational force suddenly disappers, the satellite will-

A

continue to move with the same velocity in the same orbit

B

move tangentially to the original orbit with velocity `V`.

C

fall down with increasing velocity

D

come to a stop somewhere in its original orbit

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze the motion of the satellite before and after the gravitational force disappears. ### Step-by-Step Solution: 1. **Understanding the Initial Condition**: - The satellite is in a circular orbit around the Earth, moving with a uniform velocity \( V \). This velocity is tangential to the circular path. 2. **Effect of Gravitational Force**: - The gravitational force provides the necessary centripetal force to keep the satellite in its circular orbit. This force acts towards the center of the Earth. 3. **Sudden Disappearance of Gravitational Force**: - If the gravitational force suddenly disappears, the satellite will no longer experience any centripetal force. 4. **Motion After Gravitational Force Disappears**: - According to Newton's first law of motion, an object in motion will continue to move in a straight line at constant speed unless acted upon by an external force. - Therefore, once the gravitational force is removed, the satellite will no longer follow the circular path. 5. **Resulting Path of the Satellite**: - The satellite will move in a straight line in the direction of its velocity \( V \) at the moment the gravitational force disappears. This straight-line path is tangential to the circular orbit at the point where the gravitational force was removed. ### Conclusion: The satellite will move tangentially to the original orbit with the same velocity \( V \). ---
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Knowledge Check

  • A satellite of the earth is revolving in circular orbit with a uniform velocity V. If the gravitational force suddenly disappears, the satelite will

    A
    continue to move with the same velocity in the same orbit.
    B
    move tangentially to the original orbit with velocity V.
    C
    fall down with increasing velocity.
    D
    come to a stop somewhere in its original orbit.
  • A satellite of the earth is revolving in a circular orbit with a uniform speed v . If the gravitational force suddenly disappears, the satellite will

    A
    Continue to move with velocity `v` along the original orbit
    B
    Move with a velocity `v` tangentially to the original orbit
    C
    Fall down with increases velocity
    D
    Ultimately come to rest somewhere on the original orbit
  • A satellite of the earth is revolving in a circular orbit with a uniform speed v . If gravitational force suddenly disappears, the satellite will

    A
    continue to move speed `v` along the original orbit
    B
    move with the velocity `v` tangentially to the original orbit
    C
    fall downward with increasing velocity
    D
    ultimately come to rest somewhere on the original orbit
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