0

Guest

Courses New

A rod AB of mass M and length L is lying on a horizontal frictionless surface. A particle of mass m travelling along the surface hits the end ‘A’ of the rod with a velocity V0 in a direction perpendicular to AB. The collision is elastic. After the collision the particle comes to rest. (a) Find the ratio m/M. (b) A point P on the rod is at rest immediately after collision. Find the distance AP. (c) Find the linear speed of the point P after a time p L/3V 0 after the collision.

A rod AB of mass M and length L is lying on a horizontal frictionless surface. A particle of mass m travelling along the surface hits the end ‘A’ of the rod with a velocity V0 in a direction perpendicular to AB. The collision is elastic. After the collision the particle comes to rest.
(a) Find the ratio m/M.
(b) A point P on the rod is at rest immediately after collision. Find the distance AP.
(c) Find the linear speed of the point P after a time pL/3V0 after the collision.

Grade:

2 Answers

Chetan Mandayam Nayakar
312 Points
12 years ago

Dear Jay,

after collision let linear and angular velocity of centre of rod be V and w. Let moment of inertia of rod perpendicular to rod through centre of rod be I,

mv0=MV,(v0*L/2)m=Iw

(m/2)(v0)2=(I/2)w2+(M/2)V2, solve the three equations to obtain V,w and M.

b)(lAPl-(L/2))w=V

c)at t=(pi)L/3V0 AP would have rotated by w*t

(linear speed)2=(V+((lAPl-(L/2))sin(2700-wt)))2+((lAPl-(L/2))cos(2700-wt))2

Please feel free to post as many doubts on our discussion forum as you can. If you find any question
Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We
are all IITians and here to help you in your IIT JEE preparation.


All the best Jay !!!

 


Regards,

Askiitians Experts

CHETAN MANDAYAM NAYAKAR

Rishi Sharma
askIITians Faculty 646 Points
3 years ago
Dear Student,
Please find below the solution to your problem.

after collision let linear and angular velocity of centre of rod be V and w. Let moment of inertia of rod perpendicular to rod through centre of rod be I,
mv0=MV,(v0*L/2)m=Iw
(m/2)(v0)2=(I/2)w2+(M/2)V2, solve the three equations to obtain V,w and M.

b)(lAPl-(L/2))w=V
c)at t=(pi)L/3V0 AP would have rotated by w*t
(linear speed)2=(V+((lAPl-(L/2))sin(2700-wt)))2+((lAPl-(L/2))cos(2700-wt))2

Thanks and Regards

Think You Can Provide A Better Answer ?

Other Related Questions on Mechanics

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More