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

A sphere of radius r is rolling without sliding. What is the ratio of rotational K.E. and total K.E. associated with the sphere?

A
12
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
27
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
25
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B 27
Given: A sphere of radius r is rolling without sliding.
To find the ratio of rotational K.E. and total K.E. associated with the sphere
Solution:
We know,
For an object that is rotating only, the kinetic energy is,
KErotational=12Iω2KErotational=12×25MR2v2CMR2KErotational=15Mv2CM....(i)
For an object that is rolling, i.e., translating and rotating simultaneously, the total kinetic energy of such an object is:
And KEtotal=12Mv2CM+12Iω2KEtotal=12Mv2CM+12×25MR2v2CMR2KEtotal=12Mv2CM+15Mv2CMKEtotal=5+210Mv2CMKEtotal=710Mv2CM....(ii)
So, by divinding eqn(i) and eqn(ii), we get
KErotationalKEtotal=15Mv2CM710Mv2CM=27
is the required ratio of rotational K.E. and total K.E. associated with the sphere

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Rolling
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon