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

A solid sphere of mass 7 kg rolls without slipping on an inclined plane of inclination 60. What should be the minimum coefficient of static friction to support pure rolling?

A
3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
237
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
27
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
32
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B 237

Given, the sphere is rolling without sliding. Hence,
a=αR ...(i)
From, τcom=Icomα
f×R=25mR2×α
or f=25mRα=25ma ...(ii)
[using (i)]
Applying Newton's 2nd law,
Fext=macom
mgsinθf=ma ...(iii)

Putting (1) & (ii) in (iii)
mgsinθ25ma=ma
a=5gsinθ7 & f=2mgsinθ7

We know, (fs)max=μN=μmgcosθ
and, f[(fs)max]

2mgsinθ7μmgcosθ
μ27tanθ
μmin=27tan60=237

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon