Question

A solid sphere of mass $1 \,kg$ and radius $1 \,m$ rolls without slipping on a fixed inclined plane with an angle of inclination $\theta=30^{\circ}$ from the horizontal. Two forces of magnitude $1 \,N$ each, parallel to the incline, act on the sphere, both at distance $r=0.5 \,m$ from the center of the sphere, as shown in the figure. The acceleration of the sphere down the plane is ____ $ms ^{-2}$. (Take $g=10 \,m s ^{-2}$.)

Answer 1

$ 5+1-1- f =1 a $
$ 5- f = a $
$ \text { About } COM $
$ f 1-2(1(0.5))=\frac{2}{5} Mr ^2 \alpha $
$ \Rightarrow f -1=\frac{2}{5} a$
$ \Rightarrow f =1+\frac{2}{5} a$
$ 5- a =1+\frac{2}{5} a $
$ \Rightarrow 4=\frac{7 a }{5} $
$\Rightarrow a =\frac{20}{7}=2.86\, m / s ^2$