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JEE Main & Advanced Physics Rotational Motion Question Bank Self Evaluation Test - System of Particles Rotational Motion

  • question_answer
    A bullet of mass 10 g and speed 500 m/s is fired into a door and gets embedded exactly at the centre of the door. The door is 1.0 m wide and weighs 12 kg. It is hinged at one end and rotates about a vertical axis practically without friction. The angular speed of the door just after the bullet embeds into it will be:

    A) 6.25rad/sec      

    B)        0.625 rad/sec

    C) 3.35 rad/sec      

    D)        0.335 rad/sec

    Correct Answer: B

    Solution :

    [b] \[Let\text{ }x=\]distance between hinge and centre of the door \[=L/2=\frac{1}{2}=0.5m\] As per conservation of angular momentum \[mvx=I\omega \] \[\Rightarrow w=\frac{mvx}{I}=\frac{0.01\times 500\times 0.5}{\frac{1}{3}\times 12\times {{(1)}^{2}}}=0.625rad/s\]


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