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A satellite in a force-free space sweeps stationary interplanetary dust at a rate (dM/dt) = αν. The acceleration of satellite is
- a)-2 αν2/M
- b)-αν2/M
- c)-αν2/M
- d)-αν2
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A satellite in a force-free space sweeps stationary interplanetary dus...
Acceleration of the Satellite in force-free space:
1. Given:
- Rate of sweeping of interplanetary dust, dM/dt = αν
2. Acceleration of the satellite:
- The force exerted on the satellite by the dust is F = dM/dt * v (where v is the velocity of the dust particles)
- Using Newton's second law, F = M * a, where a is the acceleration of the satellite
- Substituting the values, M * a = αν * v
- Therefore, acceleration, a = αν/M
3. Final Answer:
- The acceleration of the satellite in force-free space is given by -αν^2/M, which corresponds to option 'B' in the question.
Therefore, the correct answer is option 'B' (-αν^2/M), as the acceleration of the satellite in force-free space is proportional to the rate of sweeping of interplanetary dust.
1. Given:
- Rate of sweeping of interplanetary dust, dM/dt = αν
2. Acceleration of the satellite:
- The force exerted on the satellite by the dust is F = dM/dt * v (where v is the velocity of the dust particles)
- Using Newton's second law, F = M * a, where a is the acceleration of the satellite
- Substituting the values, M * a = αν * v
- Therefore, acceleration, a = αν/M
3. Final Answer:
- The acceleration of the satellite in force-free space is given by -αν^2/M, which corresponds to option 'B' in the question.
Therefore, the correct answer is option 'B' (-αν^2/M), as the acceleration of the satellite in force-free space is proportional to the rate of sweeping of interplanetary dust.
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