A uniform cube of side ‘b’ and mass M rest on a rough horizontal … - Vidyadip

MCQ

$A$ 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?

✓
$\mu > \frac{2}{3}$
B
$\mu > \frac{1}{3}$
C
$\mu > \frac{3}{2}$
D
none

✓

Answer

Correct option: A.

$\mu > \frac{2}{3}$

a
$\mathrm{mg} \frac{\mathrm{b}}{2}=\mathrm{F} \frac{3 \mathrm{b}}{4}$

$\mathrm{F}=\mathrm{f}<\mu \mathrm{mg} \ldots(2)$

From equation $(1)$ and $( 2)$

$\mathrm{F}<\mu \mathrm{mg}$

$\frac{2 m g}{3}<\mu g$

or $\mu>\frac{2}{3}$

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