Question

3. A round object of mass M and radius R rolls down without slipping along an inclined plane. The frictional
force
b) decreases the rotational motion
a) dissipates kinetic energy as heat
c) decreases the rotational & translational motion
d) converts translational energy into rotational energy​

Answer 1

Answer:

option d

Explanation:

According to question

mg∗sinA−f=ma--------------(1)

in pure rolling α= a/r

where α = angular acceleration

Now

net, τ=Iα where I = moment of inertia

f∗r=Iα

f∗r=Ia/r

therefore

f=Ia/r^2------------------(2)

putting value of (f) in (1)

mgsinA−Ia/r^2=ma

here I of solid cylinder = mr^2/2

mgsinA−ma/2=ma

a=(2gsinA)/3

Now

f=Ia/r^2 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

(m∗g∗sinA)/3<=μmgcosA

tanA<=3μ