A particle, moving horizontally, collides perpendicularly at one end of a rod having equal mass and placed on a smooth horizontal surface

a) |
Particle cones to rest if collision is perfectly elastic and center of rod starts to move with the same velocity |

b) |
Particle continues to move along the same direction, whatever is the value of |

c) |
Particle may get rebound back |

d) |
Velocity of mid-point of the rod will be less than if the particle gets stuck |

A particle, moving horizontally, collides perpendicularly at one end of a rod having equal mass and placed on a smooth horizontal surface

a) |
Particle cones to rest if collision is perfectly elastic and center of rod starts to move with the same velocity |

b) |
Particle continues to move along the same direction, whatever is the value of |

c) |
Particle may get rebound back |

d) |
Velocity of mid-point of the rod will be less than if the particle gets stuck |

1 Answer

5876 Votes

3537

Whenever two particles having equal mass collide head on elastically, their velocities get interchanged. Therefore, if the particle collides at midpoint of the rod, then velocities would get interchanged. In that case option (a) would be correct. But now the particle strikes at an end of the rod, hence particle head-on collision does not take place. Therefore, option (a) is incorrect It the particle gets rebound back to its original path, then its final momentum will become negative. Since mass of the particle and rod is equal, therefore law of conservation of momentum will be satisfied only when velocity of centre of mass of the rod is greater than original velocity of the particle. Hence, kinetic energy of the system (just after collision) will become greater than that (just before the collision), which is impossible. Hence, the particle cannot rebound back or it will continue but option (c) is incorrect. If the particle gets stick to the rod, centre of mass of the system will lie a distance from the end at which the particle sticks. According to the law of conservation of momentum, centre of mass will start to move with velocity . But the particle will simultaneously start to rotate about the centre of mass in an anticlockwise direction.Angular velocity of that rotational motion can be calculated by applying law of conservation of angular momentum. Hence, the resultant velocity of the midpoint of the rod will be equal to , which is obviously .Therefore option (d) is correct |

Complete the letter series: SHINE, VEMJJ, XBQFO, ? |
|||||||

(a) |
ZXTAS |
(b) |
AYUBT |
(c) |
BZVCU |
(d) |
WTUAV |

We hope we have given the updated helpful answer / content for your query in an easily accessible format to help you in preparing adequately. We do offer free support materials, 11th maths guide 11th maths guide 12th maths guide 10th maths guide, also for all the classes books and guide to all the students who sign up for SaraNextGen. Apart from traditional textbook queries, we've got conjointly provided further high order level thinking issues, that are seemingly to be expected in boards and competitive exams. It includes conceptual queries, MCQs, Long and short answer type queries, etc. These Questions are designed to learn each student and academics by providing chapter-wise further issues focusing totally on testing conceptual information with applications. Here, we've got provided a number of the necessary ways in which within which the solutions of all the Questions will profit students of class 1 to 12. If you have any queries, drop a message to us and we will get back to you at the earliest.