CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
Question

A hollow cylinder, a spherical shell, a solid cylinder and a solid sphere are allowed to roll purely on an inclined rough surface of inclination θ. The CORRECT statement(s) is/are:

A
Frictional force will be equal for all the rolling objects, if having same mass
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
If all the objects have same mass, the kinetic energy (K.E.) of all the objects will be same at the bottom of inclined plane
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
Work done by the gravitational force between the top and bottom points will be same for all, if the masses are same.
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
If cylindrical shell can roll on inclined plane, all other objects will also roll.
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D If cylindrical shell can roll on inclined plane, all other objects will also roll.
We know that for inclined plane condition,
mgsinθf=ma
Now, to satisfy the condition of pure rolling
a=rα
and fr=Iα

On substituting, we get
f=mgsinθ1+mr2I
Again, f=μmgcosθ
Therefore, on dividing both we get
μ=tanθ1+mr2I
Thus MOI for hollow cylinder is maximium of all the three objects therefore maximium μ is offered by the plane, so if it can roll all other objects will roll too.

Change in potential energy is same and no frictional loss in case of pure rolling, then applying energy conservation we can conclude that K.E. will be same at the bottom.

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