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JEE Main & Advanced Physics NLM, Friction, Circular Motion Question Bank Self Evaluation Test - Laws of Motion

  • question_answer
    A 5000 kg rocket is set for vertical firing. The exhaust speed is\[800m{{s}^{-1}}\]. To give an initial upward acceleration of\[20m{{s}^{-2}}\], the amount of gas ejected per second to supply the needed thrust will be \[\left( g=10m{{s}^{-2}} \right)\]

    A) \[127.5\text{ }kg\text{ }{{s}^{-1}}\]

    B) \[187.5\text{ }kg\text{ }{{s}^{-1}}\]

    C) \[185.5\text{ }kg\text{ }{{s}^{-1}}\]

    D) \[137.5\text{ }kg\text{ }{{s}^{-1}}\]

    Correct Answer: B

    Solution :

    [b] Given: Mass of rocket \[(m)=5000\text{ }kg\] Exhaust speed \[(v)=800\text{ }m/s\] Acceleration of rocket \[(a)=20\text{ }m/{{s}^{2}}\] Gravitational acceleration\[(g)=10\text{ }m/{{s}^{2}}\] We know that upward force \[F=m(g+a)=5000(10+20)=5000\times 30\] \[=150000\text{ N}\] We also know that amount of gas ejected \[\left( \frac{dm}{dt} \right)=\frac{F}{v}=\frac{150000}{800}=187.5\text{ }kg/{{s}^{-1}}\]


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