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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
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B
uniform cylinder
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C
uniform sphere
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D
thin spherical shell
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Solution

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=Iα------------>2
by solving those two we get,
x=Imr.
since ,
I=23mr2 for thin spherical shell;
I=25mr2 for solid spherical shell;
I=12mr2 for solid cylinder;
I=mr2 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

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