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

When a uniform solid sphere and a disc of the same mass and of the same radius rolls down without slipping on an inclined plane from rest to the same distance along the inclined plane, then the ratio of the time taken by solid sphere and the disc to cover the distance is

A
15:14
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
152:142
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
14:15
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
14:15
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C 14:15
In case of pure rolling, the acceleration of COM of the rolling bodies down the inclined plane is given by:
a=gsinθ1+K2r2=gsinθ1+Imr2 ....(i)
Now, both bodies are starting from rest u=0,ωi=0, hence applying the kinematic equation for displacement S covered along the inclined plane:
S=12at2
tspheretdisc=adiscasphere ....(ii)
From Eq. (i) and (ii):

tspheretdisc=     (1+Ispheremr2)(1+Idiscmr2) ...(iii)
Putting in Eq. (iii) Idisc=mr22, Isphere=25mr2
tspheretdisc=    1+251+12=1415
tsphere:tdisc=14:15

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