Question

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

• A. converts translational energy to rotational energy
• B. dissipates energy as heat
• C. decreases the rotational motion
• D. decreases the rotational and translational motion

Answer 1

Answer: (A)

converts translational energy to rotational energy

Answer 2

We have,
mg$\times$sinA−f=ma ________________________ (1)
in pure rolling $\alpha$ =$\frac{a}{r}$
$\alpha$ = angular acceleration
Now,τ=I$\alpha$
I = moment of inertia
f$\times$r = I$\alpha$
f$\times$r = I$\frac{a}{r}$
$\therefore$ f =Iar2 ________________________________ (2)
Substituting (2)in (1)

we have mgsinA−I$\frac{a}{r^2}$=ma

here I of solid cylinder=$\frac{mr^2}{2}$

mgsinA−$\frac{ma}{2}$=ma

a=$\frac{(2gsinA)}{3}$
Now
from (2) we have
f =$\frac{la}{r^2}$
f =$\frac{ma}{2}$ 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)

\frac{ma}{2}$$\leq $\mu$mgcosA

putting value of a

$\frac{(m\times g \times \sin A)}{3}$ $\leq$ $\mu$mgcosA
tanA $\leq$ 3μ

Therefore, the correct option is (A): converts translational energy to rotational energy