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Question

A sphere of mall 5 kg rolls without slipping on an inclined plane of inclination 30. Choose the correct statement(s).


  1. Force of friction acting on sphere is 5g7.
  2. Linear acceleration of sphere down the plane is 5g14.
  3. For pure rolling, μ>0.165.
  4. None of these 


Solution

The correct options are
A Force of friction acting on sphere is 5g7.
B Linear acceleration of sphere down the plane is 5g14.
C For pure rolling, μ>0.165.

N= Normal force
f= friction force
mg= weight of sphere
Let the linear acceleration of the sphere down the plane be a.
So, equation of linear motion for the centre of mass 
mgsinθf=ma.....(1)
Sphere rolls without slipping 
So α=ar
where α=Angular acceleration,
a=Linear acceleration

For Rotational motion, 
τ0=Iα
where τ0= Torque about centre of mass
fr=25mr2(ar)
f=25ma......(2)
From eq (1) & (2)
mgsinθ=75ma
a=57gsinθ=57×g×sin30=514g
a=5g14
and f=27mgsinθ=27×5×g×12=5g7
f=5g7
For pure rolling,
fmaxfkinetic
μmgcosθ27mgsinθ
μ27tan θ=0.165
i.e μ>0.165
Options A, B & C are correct.

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