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A uniform cube of side a and mass m rest...

A uniform cube of side a and mass `m` rests on a rough horizontal table. A horizontal force `F` is applied normal to one of the faces at a point directly above the centre of the face, at a height `(3a)/(4)` above the base. What is the minimum value of `F` for which the cube begins to tip about an edge?

Text Solution

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In the limiting case normal rection will pass through `O`. The cube will tip about `O` if torque of `F` exceeds the torque of mg.

Hence, `F((3a)/4)gtmg(a/2)` or `Fgt2/3mg`
Therefore, minimum value of `F` is `2mg//3`
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Knowledge Check

  • A uniform cube of side a and mass m rests on a rough horizontal table. A horizontal force F is applied normal to one of the faces at a point that is directly above the centre of the face, at a height (3a)/(4) above the base. The minimum value of F for which the cube begins to tilt about the edge is (assume that the cube does not slide)

    A
    `(mg)/(4)`
    B
    `(2mg)/(3)`
    C
    `(3mg)/(4)`
    D
    mg

  • A uniform cube of side and mass m rests on a rough horizontal surface. A horizontal force F is applied normal to one face at point that is directly above the centre of the face at a height (a)/(4) above the centre. The minimum value of F for which the cube begins to topple above an edge without sliding is

    A
    `(1)/(4)mg`
    B
    2mg
    C
    `(1)/(2)mg`
    D
    `(2)/(3)mg`

  • A uniform cube of side 'b' and mass M rest on a rough horizontal table. A horizontal force F is applied normal to one of the face at a point, at a height 3b//4 above the base. What should be the coefficient of friction (mu) between cube and table so that is will tip about an edge before it starts slipping ? .

    A
    `mu gt (2)/(3)`
    B
    `mu gt (1)/(3)`
    C
    `mu gt (3)/(2)`
    D
    none

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