Question

A disc and a solid sphere of same mass and radius roll down an inclined plane. The ratio of the friction force acting on the disc and sphere is?

• A. $\frac{7}{6}$
• B. $\frac{5}{4}$
• C. $\frac{3}{2}$
• D. depends on angle of inclination

Answer 1

Answer: (A)

$\frac{7}{6}$

$f=\frac{mg\sin \theta }{1+m{R}^2/I}$
$f_{disc}=\frac{mg\sin \theta }{1+2}=\frac{1}{3}mg\sin \theta$
$f_{Sphere}=\frac{mg\sin \theta }{1+5/2}=\frac{2}{7}mg\sin \theta$
$\therefore$ The ratio is $\frac{7}{6}$