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A bullet of mass 10 g and speed 500 m/s ...

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. Find the angular speed of the door just after the bullet embeds into it.

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Verified by Experts

The correct Answer is:
`0.625" rad s"^(-1)`
The moment of inertia of the door about the vertical axis at one end is `ML^(2)//3`.
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NCERT GUJARATI-SYSTEMS OF PARTICLES AND ROTATIONAL MOTION-EXERCISES
  1. (a) A child stands at the centre of a turntable with his two arms outs...

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  2. A rope of negligible mass is wound round a hollow cylinder of mass 3 k...

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  3. To maintain a rotor at a uniform angular speed of 200 rad s-1, an engi...

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  4. From a uniform disk of radius R, a circular hole of radius R/2 is cut ...

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  5. A metre stick is balanced on a knife edge at its centre. When two coin...

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  6. A solid sphere rolls down two different inclined planes of the same he...

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  7. A hoop of radius 2 m weighs 100 kg. It rolls along a horizontal floor ...

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  8. The oxygen molecule has a mass of 5.30 × 10^(-26) kg and a moment of i...

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  9. A solid cylinder rolls up an inclined plane of angle of inclination 30...

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  10. As shown in Fig.7.40, the two sides of a step ladder BA and CA are 1.6...

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  11. A man stands on a rotating platform, with his arms stretched horizonta...

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  12. A bullet of mass 10 g and speed 500 m/s is fired into a door and gets ...

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  13. Two discs of moments of inertia I(1) and I(2) about their respective a...

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  14. (a) Prove the theorem of perpendicular axes. (b) Prove the theorem o...

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  15. Prove the result that the velocity v of translation of a rolling body ...

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  16. A disc rotating about its axis with angular speed ω(o) is placed light...

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  17. Explain why friction is necessary to make the disc in Fig. 7.41 roll i...

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  18. A solid disc and a ring, both of radius 10 cm are placed on a horizont...

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  19. A cylinder of mass 10 kg and radius 15 cm is rolling perfectly on a pl...

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  20. Separation of Motion of a system of particles into motion of the centr...

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