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

A cylinder of mass 10kg and radius 15cm is rolling perfectly on a plane of inclinato of 30o. The coefficient of static friction μk=0.25. If the inclination θ of the plane is increased, at what value of θ does the cylinder begin to skid, and not roll perfectly?

A
37o
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
53o
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
90o
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
0o
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A 37o
Given: a cylinder of mass 10kg and radius 15cm is rolling perfectly on a plane of inclination of 30o. The coefficient of static friction μk=0.25
To find: if the inclination θ of the plane is increased, at what value of θ does the cylinder begin to skid, and not roll perfectly
Solution:
As per the given condition,
m=10kg
r=0.15m
μk=0.25
θ=30
I=12mr2
Acceleration of the cylinder is given as:
a=mgsinθm+Ir2a=mgsinθm+12mr2r2a=mgsinθm+12ma=mgsinθ32ma=23gsin30a=23×9.8×12a=3.27m/s2
For rolling without skid, we have the relation
μ=13tanθtanθ=3μ=3×0.5θ=tan1(0.75)=36.8737
is the value of θ for which the cylinder begin to skid, and not roll perfectly

1003718_1033534_ans_843eb98776424c25b653335010a755e2.png

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Friction: A Quantitative Picture
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon