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A rigid body of radius R, either hollow ...

A rigid body of radius R, either hollow or solid, lies on a smooth horizontal surface. The body is pulled form rest by a horizontal force acting tengentially from the highest point. The distance travelled by the body in the time in which it makes one full rotation is the same that it will make in one full rotation during pure rolling. The rigid body will be

A

solid sphere

B

hollow sphere

C

circular disc

D

hollow cylinder

Text Solution

Verified by Experts

The correct Answer is:
4
`tau=FxxR=Ialpha`
In one full rotation ,
`theta=2pi =1/2 alphat^(2)`
`t^(2)=(4pi)/(alpha) =(4piI)/(FR)`

Linear acceleration, a=F/m
Distance travelled in one rotation
`=2piR` (given)
`=1/2 at^(2) =1/2 F/M.(4pil)/(FR)=(2piI)/(MR)`
It gives `I=MR^(2)`
It is a hollow cylinder
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Knowledge Check

  • 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

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    A
    `2piR`
    B
    `8R`
    C
    `2R`
    D
    `piR`

  • A sphere cannot roll on a smooth inclined surface. The motion of a rigid body which is pivoted or fixed in some way is rotation.

    A
    If both assertion and reason are true and reason is the correct explanation of assertion.
    B
    If both assertion and reason are reason are true but reason is not the correct explanation of assertion.
    C
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