Consider a uniform cubical box of side a on a rough floor that is to be moved by applying minimum possible force F at a point b above its center of mass (see$$ $$figure). If the coefficient of friction is μ$$=0.4$$, the maximum possible value of $$100$$×ba for box not to topple before moving is $$_____$$

Question

Consider a uniform cubical box of side a on a rough floor that is to be moved by applying minimum possible force F at a point  b above its center of mass (see$$ $$figure). If the coefficient of friction is  μ$$=0.4$$, the maximum possible value of  $$100$$×ba for box not to topple before moving is $$_____$$

Infinity Learn · Accepted Answer

Sliding should not occur , $$F=$$μmg                        ...............$$.1$$​Toppling should not occur, $$Fb+a2=mga2$$         ..............$$.2$$⇒μ$$mgb+a2=mg$$×$$a2$$​⇒$$b+a2$$μ$$=a2$$⇒$$0.4=$$μ$$=a2b+a$$​⇒$$0.8b+0.4a=a$$⇒$$0.8b=0.6a$$         ​⇒$$ba=34$$  ⇒ba×$$100=34$$×$$100=75$$

Rotational motion

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Rotational motion

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Consider a uniform cubical box of side a on a rough floor that is to be moved by applying minimum possible force F at a point b above its center of mass (see figure). If the coefficient of friction is μ=0.4, the maximum possible value of 100×ba for box not to topple before moving is _____

Sliding should not occur , F=μmg ................1​Toppling should not occur, Fb+a2=mga2 ...............2⇒μmgb+a2=mg×a2​⇒b+a2μ=a2⇒0.4=μ=a2b+a​⇒0.8b+0.4a=a⇒0.8b=0.6a ​⇒ba=34 ⇒ba×100=34×100=75

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