A solid cylinder of mass M and radius R pure rolls on a rough surface as shown in the figure. Choose the correct alternative (s).

Options

A. The magnitude of the frictional force is` F//3`.
B. The frictional force on the sphere acts forward.
C. The acceleration of the centre of mass is `2F//3M`
D. The acceleration of the centre of mass is `F//M`.

Answer

A, B, C, D

Explanation

Acceleration of centre of mass
`a_(c)=F/m1/(1+(K^(2))/(R^(2)))=(5F)/(7M)` (`:'K=sqrt(2/5R)`

Frictional foce `f=F[1/(1+(R^(2))/(K^(2)))]=(2F)/7`
Since`f=+ve` frictioin is directed backward.
options `a,b,c, d` are incorrect so option `a,b, c` and `d` are the correct options.