Home
Class 12
PHYSICS
A small ball of mass m hits the cylinder...


A small ball of mass m hits the cylinder which is hinged at top and free to rotate in vertical plane as shown in figure. Mass of cylinder is M. Linear momentum of system (ball+cylinder)

A

Remains conserved if y=R

B

Remains conserved if `y=(3)/(2)R`

C

Remains conserved if `y=(7)/(5)R`

D

Cannot be conserved for any value of y.

Text Solution

Verified by Experts

The correct Answer is:
B
muy`=mVy+(3)/(2)MR^(2)omega` where u is speed of ball before collision, V speed of ball after collision and `omega` is angular speed of cylinder after collision.
`m u=mV+Mromega(COM)`
`thereforey=(3R)/(2)`
Promotional Banner

Topper's Solved these Questions

  • TEST PAPERS

    FIITJEE|Exercise PHYSICS|747 Videos

  • SIMPLE HARMONIC MOTION

    FIITJEE|Exercise Assignment Problems (Objective) (Level-II)|20 Videos

  • WORK, ENERGY AND POWER

    FIITJEE|Exercise COMPREHENSIONS ( Comprehension-II)|5 Videos

Similar Questions

Explore conceptually related problems

A rigid rod of mass m with a ball of mass M attached to the free end is restrained to oscillate in a vertical plane as shown in the figure. Find the natural frequency of oscillation.

A ball of mass m is attached to a string whose other end is fixed. The system is free to rotate in vertical plane. When the ball swings, no work is done on the ball by the tension in the string. Which of the following statement is the correct explanation?

An cylinder of mass m is rotated about its axis by an angular velocity omega and lowered gently on an inclined plane as shown in figure. Then : .

A solid cylinder of mass m is wrapped with an inextensible light string and, is placed on a rough inclined plane as shown in the figure. The frictional force acting between the cylinder and the inclined plane is : [The coefficient of static friction, mu_(s)" is 0.4"]

A rectangular rigid fixed block has a long horizontal edge. A solid homogeneous cylinder of radus R is placed horizontally at rest its length parallel to the edge such that the exis of the cylinder and the endg of the block are in the same vertical plane as shown in the figure below. Ther is sufficinet friction present at the edge s that a very small displacement causes the cylinder to roll off the edge without slipping. Determine: (a) the angle theta_c through which the cylinder rotates before it leaves contact with the edge, (b) the speed of the centre of mass of the cylinder before leaving contact with the edge, and (c) the ratio of the translational to rotational kinetic energy of the cylinder when its centre of mass is in horizontal line with the edge.

A solid cylinder of mass 20 kg rotates about its axis with angular speed 100 s^(-1) . The radius of the cylinder is 0.25 m . What is the kinetic energy associated with the rotation of the cylinder ? What is the magnitude of angular momentum of the cylinder about its axis ?

A uniform rod ofmass M and length L is hanging from its one end free to rotate in a veritcal plane.A small ball of equal mass is attached of the lowe end as shown. Time period of small oscillations of the rod is

FIITJEE-TEST PAPERS-PHYSICS
  1. A body (solid sphere) of mass m makes an elastic collision with anothe...

    Text Solution

    |

  2. A simple pendulum of mass m charged negatively to q coulomb oscillates...

    Text Solution

    |

  3. A small ball of mass m hits the cylinder which is hinged at top and fr...

    Text Solution

    |

  4. A charge particle q of mass is placed at a distance d from another cha...

    Text Solution

    |

  5. A thin, uniform rod of mass M and length L is at rest on a smooth hori...

    Text Solution

    |

  6. In the shown diagram two point masses m are joined by a massless rod o...

    Text Solution

    |

  7. A battery of emf E(0) = 12 V is connected across a 4 m long uniform wi...

    Text Solution

    |

  8. A uniform rod of length L and mass M is pivoted freely at one end and ...

    Text Solution

    |

  9. A whel of mass 2kg an radius 10 cm is rotating about its axis at an an...

    Text Solution

    |

  10. A hydrogen atom emits a photon corresponding to an electron transition...

    Text Solution

    |

  11. A plane wave front of light is incident on a plane mirror. Intensity i...

    Text Solution

    |

  12. An X-ray tube has three main controls. (i). The target material (its...

    Text Solution

    |

  13. The image of an object, formed by a plano-convex lens at a distance of...

    Text Solution

    |

  14. A long straight wire, carrying current I, is bent at its midpoint to f...

    Text Solution

    |

  15. A steel wire of length 60 cm and area of cross section 10^(-6)m^(2) is...

    Text Solution

    |

  16. A cubical frame is made by connecting 12 identical uniform conducting ...

    Text Solution

    |

  17. A body of mass 1kg is suspended from a weightless spring having force ...

    Text Solution

    |

  18. The figure shows a system of two concentric spheres of radii r1 and r2...

    Text Solution

    |

  19. Two spherical bodies of mass M and 5M & radii R & 2R respectively are ...

    Text Solution

    |

  20. A tunnel is dug along a chord of the earth at a perpendicular distance...

    Text Solution

    |