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A cube is resting on an inclinded plane....

A cube is resting on an inclinded plane. If the angle of inclination is gradually increased. What must be the coefficient of friction between the cube and plane so that,
(a). Cube slides before toppling?
(b). Cube topplies before sliding?

Text Solution

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For sliding `mgsinthetagtmumgcostheta`
or `tanthetagtmu` ..(i)
for toppling ltbr. `tau_(mgsintheta)gttau_(mgcostheta)`
`therefore(mgsintheta)((a)/(2))gt(mgcostheta)((a)/(2))` ltbr. Or `tanthetagt1` ..(ii)
if `mugt1` then condition (ii) is satisfied earlier So, the cube topples before sliding.
if `mult1` then condition (i) is satisfied earlier. So, the cube slides before toppling.
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