1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# A solid sphere A of mass m rolls without slipping on an inclined plane of inclination 30∘. Coefficient of friction of the inclined plane is μ. Then, which of the following options is satisfied when the sphere undergoes pure rolling motion?

A
μ237
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
μ273
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
μ<237
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
μ<273
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is B μ≥27√3Le us assume the radius of the sphere is R. F.B.D from the data given in the question is shown below. From the diagram, we can deduce that ∑Fx=max [Net Force along x - direction] ⇒mgsinθ−f=ma ......(1) ∑Fy=may [Net Force along y - direction] ⇒N=mgcosθ .....(2) Torque experienced by the sphere due to frictional force is given by fR=Iα where I= Moment of inertia of solid sphere =25mR2 ⇒fR=(25mR2)(aR) [∵α=aR] ⇒f=25ma ......(3) Substituting (3) in (1), mgsinθ−25ma=ma ⇒gsinθ=(a+25a) ⇒gsinθ=75a ⇒a=57gsinθ and from (3), we can say that f=27mgsinθ .....(4) For pure rolling, μN≥f From (2) and (4) μmgcosθ≥27mgsinθ ⇒μ≥27tan θ ⇒μ≥27tan 30∘ ⇒μ≥27√3 Hence, option (b) is the correct answer.

Suggest Corrections
0
Join BYJU'S Learning Program
Explore more
Join BYJU'S Learning Program