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Physics

Mechanics

Easy

Question

A cubical block of side L and mass m is placed on a horizontal floor. In the arrangement as shown, a force F is applied at the end of the plane sheet PQ which is firmly attached with the block. What should be the minimum value of PQ so that block may be tipped about an edge?

$L / \sqrt{3}$
$L / \sqrt{2}$
$L \sqrt{2} / 3$
$L \sqrt{3} / \sqrt{2}$

The correct answer is: $L divided by square root of 3$

$B l o c k space w i l l space b e space t i p p e d space a b o u t space p o i n t space O. table attributes columnalign left columnspacing 1em rowspacing 4 pt end attributes row cell M subscript 0 equals open parentheses F cos invisible function application 30 to the power of ring operator close parentheses a equals F sin invisible function application 30 to the power of ring operator L plus m g L divided by 2 end cell row cell F equals fraction numerator m g L over denominator left parenthesis a square root of 3 minus L right parenthesis end fraction end cell row cell text For end text F greater than 0 comma a square root of 3 greater than L semicolon space of 1em a greater or equal than L divided by square root of 3 end cell end table$

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