wiz-icon
MyQuestionIcon
MyQuestionIcon
7
You visited us 7 times! Enjoying our articles? Unlock Full Access!
Question

A uniform bar of negligible cross sectional area of length 6a and mass 8m lies on a horizontal frictionless table. Two point masses m and 2m moving in opposite directions but in the same horizontal plane with speeds 2v and v respectively strike the bar at a distance a and 2a from one end and stick to the bar after the collision. Then, after the collision,


A
The velocity of centre of mass is 4 ms1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
The angular speed of the bar with the masses stuck to it is v15a
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

The moment of inertia of the bar with masses stuck to it about the axis passing through the centre of the bar and perpendicular to its plane is 30ma2

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
The total energy of the bar is 325mv2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C

The moment of inertia of the bar with masses stuck to it about the axis passing through the centre of the bar and perpendicular to its plane is 30ma2


Since no external force is applied, the linear momentum is conserved. Hence, VCM=0
Moment of inertia of the system is,
I=2ma2+m(2a)2+[112×8m×(6a)2]=30ma2
Since no external torque is applied, the angular momentum of the system is conserved.
(2mv×a)+(m×2v×2a)=Iw
6 mva=30 ma2ww=v5a
=12Iw2
=12(30a ma)(V5a)2=35 mv2

flag
Suggest Corrections
thumbs-up
0
similar_icon
Similar questions
View More
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Relative
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon