Variable Mass Systems & Rocket Motion questions with solutions

Showing 1–10 of 13 questions

• MCQmediumCenter of maas , Momentum and CollisionVariable Mass Systems & Rocket Motion

  An open wagon of mass 5×10⁴ kg moves at 1.2 m s⁻¹ on a frictionless track. Rain falls vertically into it. After collecting 10⁴ kg water, its speed is:

  Options

  • Option A

    0.5 m s⁻¹

  • Option B

    2 m s⁻¹

  • Option C

    1 m s⁻¹

  • Option D

    1.5 m s⁻¹

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• NumericeasyCenter of maas , Momentum and CollisionVariable Mass Systems & Rocket Motion

  A rocket in deep space ejects gases with speed 100 m/s relative to itself. Its mass decreases from M0 to M0/2. If its increase in speed is N ln2 m/s, find N.

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• MCQmediumCenter of maas , Momentum and CollisionVariable Mass Systems & Rocket Motion

  A rocket moves in deep space with negligible external force. Its exhaust speed relative to the rocket is u. Its mass decreases from $M_0$ to M. The increase in the rocket's speed is:

  Options

  • Option A

    u ln($M_0$/M)

  • Option B

    u($M_0$-M)/M

  • Option C

    u ln(M/$M_0$)

  • Option D

    uM/$M_0$

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• Multi-correctmediumCenter of maas , Momentum and CollisionVariable Mass Systems & Rocket Motion

  A trolley containing sand moves on a perfectly smooth horizontal track. Sand leaks vertically downward through a hole in the trolley. Assume each sand particle has the same horizontal velocity as the trolley at the instant it leaves. Which statements are correct?

  Select all that apply

  • Option A

    The horizontal speed of the trolley remains constant

  • Option B

    Loss of mass alone does not necessarily accelerate the trolley

  • Option C

    The escaping sand carries horizontal momentum

  • Option D

    The trolley must accelerate because its mass is decreasing

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• MCQmediumCenter of maas , Momentum and CollisionVariable Mass Systems & Rocket Motion

  A rocket is fired vertically upward. The exhaust speed relative to the rocket is u. During a time t, its mass decreases from M$M_0$ to M. Neglect air resistance and take g constant. If its initial speed is zero, its speed after time t is:

  Options

  • Option A

    u ln($M_0$/M) - gt

  • Option B

    u ln($M_0$/M) + gt

  • Option C

    u($M_0$-M)/M - gt

  • Option D

    u ln(M/$M_0$) - gt

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• NumericmediumCenter of maas , Momentum and CollisionVariable Mass Systems & Rocket Motion

  A rocket of instantaneous mass 100 kg ejects fuel backward at a rate 4 kg/s with relative exhaust speed 500 m/s. Neglect gravity. If its instantaneous acceleration is N m/s², find N.

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• NumericmediumCenter of maas , Momentum and CollisionVariable Mass Systems & Rocket Motion

  Water of density 1000 kg/m³ is discharged horizontally from a stationary nozzle of cross-sectional area 2 cm² with speed 20 m/s. If the magnitude of the reaction force on the nozzle is N newton, find N.

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• NumericmediumCenter of maas , Momentum and CollisionVariable Mass Systems & Rocket Motion

  Water flows through a smooth stationary 90° pipe bend at a constant mass rate 2 kg/s. Its speed is 10 m/s before and after the bend. Initially the velocity is along +x, and after the bend it is along +y. Neglect pressure-force differences and gravity. If the magnitude of the force exerted by water on the pipe is N√2 newton, find N.

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• MCQmediumCenter of maas , Momentum and CollisionVariable Mass Systems & Rocket Motion

  In a rocket, 1000 kg of fuel is consumed at 40 kg s⁻¹ and gases are ejected at 5×10⁴ m s⁻¹. The thrust on the rocket is approximately:

  Options

  • Option A

    2×10⁴ N

  • Option B

    5×10⁵ N

  • Option C

    2×10⁶ N

  • Option D

    2×10⁷ N

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• ParagraphmediumCenter of maas , Momentum and CollisionVariable Mass Systems & Rocket Motion

  A car has initial total mass 50 kg. Gases are ejected backward at relative speed 20 m s⁻¹ at 2 kg s⁻¹; total ejected gas is 20 kg. Coefficient of friction with road is μ = 0.1. Use the variable-mass thrust relation.

  

  Sub-question 1

  Car starts moving after:

  Options

  • Option A

    4 s

  • Option B

    10 s

  • Option C

    5 s

  • Option D

    8 s

  Sub-question 2

  Maximum speed of the car is: (Take ln(4/3)=0.28)

  Options

  • Option A

    0.6 m s⁻¹

  • Option B

    0.8 m s⁻¹

  • Option C

    1.0 m s⁻¹

  • Option D

    1.2 m s⁻¹

  Sub-question 3

  Car stops after, measured from the instant it starts moving:

  Options

  • Option A

    12.2 s

  • Option B

    6.4 s

  • Option C

    10.6 s

  • Option D

    5.8 s

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