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Question

A drum of radius R and mass M, rolls down without slipping along an inclined plane of angle θ. The frictional force

A
Converts transnational energy to rotational energy
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B
Dissipates energy has heat
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C
Decreases the rotational motion
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D
Deceases the rotational and translation motion
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Solution

The correct option is A Converts transnational energy to rotational energy
According to question
mgsinAf=ma--------------(1)
in pure rolling α=ar where α = angular acceleration
Now
net, τ=Iα where I = moment of inertia
fr=Iα
fr=Ia/r
therefore
f=Ia/r2. -------------------(2)
putting value of f in (1)
mgsinAIa/r2=ma
here I of solid cylinder = mr2/2
mgsinAma/2=ma
a=(2gsinA)/3
Now
f=Ia/r2 from (2)
f=ma/2 which should be less than or equal to μN otherwise body will slip (where u is coefficient of friction and N is normal acting on cylinder which is equal to mg cos A)
ma/2<=μmgcosA
putting value of a

(mgsinA)/3<=μmgcosA
tanA<=3μ



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