Question

A body kept on a smooth horizontal surface is pulled by a constant horizontal force applied at the top point of the body. If the body rolls purely on the surface, its shape can be:

• A. thin pipe
• B. uniform cylinder
• C. uniform sphere
• D. thin spherical shell

Answer 1

The correct option is A thin pipe

Let $F$ be the force acting on a body . Let O be the centre of body.
Now lets search for , value of distance between line of action of and centre of body so that body starts slip from rolling.(say "$x$")
$F=ma$ {Newton's law of motion}------->1
$Fx=I$$\alpha$------------>2
by solving those two we get,
$x=$$\frac{I}{mr}$.
since ,
$I=$$\frac{2}{3}m{r}^2$ for thin spherical shell;
$I=$$\frac{2}{5}m{r}^2$ for solid spherical shell;
$I=$$\frac{1}{2}m{r}^2$ for solid cylinder;
$I=$$m{r}^2$ for thin pipe.
by substituting,
only thin pipe satisfies the above condition of rolling if force is applied on the top of body.
Therefore,Option A is answer