wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

A circular disc of mass M and radius R is rotating about its axis with angular speed ω. If another stationary disc having radius R2 and same mass M is dropped co-axially on to the rotating disc. Gradually, both discs attain constant angular speed ωf. The energy lost in the process is p% of the initial energy. The value of p is (integer only)

Open in App
Solution

As we know moment of inertia disc, Idisc=12MR2


Using angular momentum conservation,

I1ω1+I2ω2=(I1+I2)×ωf
MR22×ω+0=(MR22+MR28)ωf
ωf=45ω
Initial K.E., Ki=12Iω2=12(MR22)ω2=MR2ω24
Final K.E., Kf=12(MR22+MR28)1625ω2=MR2ω25

Percentage % loss in kinetic energy is,

%=KEiKEfKEi=MR2ω24MR2ω25MR2ω24×100=20%=p%
Hence, value of p=20

flag
Suggest Corrections
thumbs-up
19
similar_icon
Similar questions
View More
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Rotational Kinematics
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon