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A satellite in force free space sweeps stationary interplanetary dust at a rate dM/dt = αv where M is the mass and v is the velocity of the satellite and α is a constant. What is the deceleration of the satellite? [1994]
- a)-αv2
- b)-αv2/2M
- c)-αv2/M
- d)-2αv2/M
Correct answer is option 'C'. Can you explain this answer?
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A satellite in force free space sweeps stationary interplanetary dust ...
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A satellite in force free space sweeps stationary interplanetary dust ...
Deceleration of the Satellite:
- Given: dM/dt = αv, where M is the mass and v is the velocity of the satellite, and α is a constant.
- The force acting on the satellite is equal to the rate of change of momentum.
- The force is given by F = dp/dt = d(Mv)/dt
- Using the product rule, we get F = v dM/dt + M dv/dt
- Substituting dM/dt = αv, we get F = αv^2 + M dv/dt
- The deceleration of the satellite is the acceleration in the opposite direction of its motion, so it is -dv/dt.
- Therefore, the deceleration, -dv/dt, is equal to F/M - αv^2/M = -αv^2/M
Therefore, the deceleration of the satellite is -αv^2/M, which corresponds to option 'c'.
- Given: dM/dt = αv, where M is the mass and v is the velocity of the satellite, and α is a constant.
- The force acting on the satellite is equal to the rate of change of momentum.
- The force is given by F = dp/dt = d(Mv)/dt
- Using the product rule, we get F = v dM/dt + M dv/dt
- Substituting dM/dt = αv, we get F = αv^2 + M dv/dt
- The deceleration of the satellite is the acceleration in the opposite direction of its motion, so it is -dv/dt.
- Therefore, the deceleration, -dv/dt, is equal to F/M - αv^2/M = -αv^2/M
Therefore, the deceleration of the satellite is -αv^2/M, which corresponds to option 'c'.
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A satellite in force free space sweeps stationary interplanetary dust at a rate dM/dt = αv where M is the mass and v is the velocity of the satellite and α is a constant. What is the deceleration of the satellite? [1994]a)-αv2b)-αv2/2Mc)-αv2/Md)-2αv2/MCorrect answer is option 'C'. Can you explain this answer?
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