Last Updated On [03-11-2023]
A uniform rod of length 
and mass 
rests on a smooth horizontal table. A point mass 
moving horizontally at right angles to the rod with initial velocity 
collides with one end of the rod and sticks to it
|
Determine the angular velocity of the system after the collision |
|||||||
|
a) |
|
b) |
|
c) |
|
d) |
|
Question ID - 101303 :- A uniform rod of length and mass rests on a smooth horizontal table. A point mass moving horizontally at right angles to the rod with initial velocity collides with one end of the rod and sticks to it
Determine the angular velocity of the system after the collision
a)
b)
c)
d)
A uniform rod of length and mass rests on a smooth horizontal table. A point mass moving horizontally at right angles to the rod with initial velocity collides with one end of the rod and sticks to it
|
Determine the angular velocity of the system after the collision |
|||||||
|
a) |
|
b) |
|
c) |
|
d) |
|
(a)
After collision, the centre of mass of the composite system will move in a straight line with a constant speed and the system will rotate with a constant angular velocity about the vertical axis passing through (and translating with) the centre of mass of the system. During the collision, the external force and torque about any point (or axis) in an inertial reference frame is zero. The torque acting on the system in the centre of mass reference frame is also zero
.png)
There are many (mathematically infinite) points (axes) about which the angular momentum of the system remains constant during the collision. The centre of mass of the composite system is the most convenient point
The distance of the centre of mass of the system from the end where 
sticks is given by
Let the velocity of the centre of mass of the system after collision be 
and the angular velocity of the system about the vertical axis through the centre of mass be 
as shown in the figure
From the conservation of the angular momentum about the centre of mass axis
(i)
Moment of inertia of the composite system about the centre of mass axis is
(ii)
From Eqs. (i) and (ii)
Next Question :
There are three words. The first two words to the left of (: :) are related in some way. The same relationship holds between the third word to the right of sign (: :) and one of the responses. Identify the correct related word.
|
Calendar : Dates : : Dictionary : ? |
|||||||
|
(a) |
Language |
(b) |
Sentences |
(c) |
Grammar |
(d) |
Vocabulary |
View Topper Answer
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.
