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A ring and a disc of same mass m and sam...

A ring and a disc of same mass `m` and same radius `R` are joinged concentrically. This system is placed on a smooth plane with the common axis parallel to the plane as shown in figure. A horizontal force `F` is applied on the system at a point which is at a distance `x` from the centre. The value of `x` so that it starts pure rolling is

A

`(R)/(2)`

B

`(3R)/(4)`

C

`R`

D

Pure rollong is not possible as the floor is smooth.

Text Solution

Verified by Experts

The correct Answer is:
B
`a_(cm)=(F)/(2m)alpha=(F.x)/((mR^(2))/(2)+mR^(2))=(2F.x)/(3mR^(2))`
`a_(cm)=alphaR`
`(F)/(2m)=(2Fx)/(3mR^(2))R, x=(3R)/(4)`
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Knowledge Check

  • A hollow cylinder of mass m and radius r is kept on a smooth horizontal surface. Horizontal force F is applied at a height above the centre. Find the value of h/R so that ring performs pure rolling on the surface.

    A
    1
    B
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    C
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    D
    `2/5`

  • A uniform circular disc of radius R is placed on a smooth horizontal surface with its plane horizontal and hinged at circumference through point O as shown . An impulse P is applied at a perpendicular distance h from its centre C. The value of h so that the impulse due to hinge is zero, is

    A
    `R`
    B
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    C
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    D
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  • An inverted T -shaped object is placed on a horizontal floor as shown in Fig. A force F is applied on the system as shown in Fig. The value of x so that the system performs pure translational motion is

    A
    `L/4`
    B
    `(3L)/4`
    C
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    D
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