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 $r=05 \,m$ 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

Solid sphere 1kg, 1m

$5 + 1 – 1 – f = 1a$
$5 – f = a$
About COM
$f 1 – 2(1(0.5)) =\frac{2}{5}Mr^2\alpha$
⇒$$f-1=\frac{2}{5}a
$⇒f=1+\frac{2}{5}a$
$⇒ 4-\frac{7a}{5}$
$⇒a=\frac{20}{7}=2.86$

Hence,the acceleration of the sphere down the plane is 2.86 ms-2.