truck is moving with accleration "a".Cylinder at back has mass "m" and radius "r". Friction is just enough to avoid slipping.find the distance covered by truck in the time, the cylinder falls of the truck.Also solve the question taking sphere in place of cylinder.

a seudo force acts at the center of mass of the body placed on the truck...

let moment of inertia of this body is I ....

friction will act rightwards & seudo force will also act rightwards...

seudo force (F)=ma

F + f = ma¹ ............1

    fr = I(alfa) ...........2                     

f is friction force  & alfa is angular acclaration

for pure rolling a¹ = (alfa)r

so

       f = a¹I/r²  ........3

solving 1 & 3 we get

 a¹ = F/(m - I/r²)     ...............4

now this object will have constant accleration a¹

it will fall when after covering d distance so

 d = a¹t²/2

t² = 2d/a¹ ...........5

during this period truck has covered some distance so

distance covered by truck(S) =at²/2                  (accleration of truck is a)

                                    S = ad/a¹ =ad(m-I/r²)/F

                                                   =d(m-I/r²)

if it is a cylinder  then S = dm/2

if it is sphere then S = 3md/5

the ans is 3d/2.

also plz explain how the direction of friction is decided ??