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  4. A horizontal force F is applied at the top of an equilateral triangular block having mass m. The minimum coefficient of friction required to topple the block before translation will be <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-fqpuaglowsajcq7g.jpg />

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Q. A horizontal force $F$ is applied at the top of an equilateral triangular block having mass $m.$ The minimum coefficient of friction required to topple the block before translation will be
Question

NTA AbhyasNTA Abhyas 2022

Solution:

$I=\frac{m a^{2}}{6}+m\left(\frac{a}{\sqrt{3}}\right)^{2}\Rightarrow I=\left(\frac{m a^{2}}{2}\right)$
$\Rightarrow F\times \frac{a \sqrt{3}}{2}=\left(m g\right)\frac{a}{2}\Rightarrow F=\left(\frac{m g}{\sqrt{3}}\right)$
$F=F_{m a x}\Rightarrow \frac{m g}{\sqrt{3}}=\mu mg\Rightarrow \mu =\frac{1}{\sqrt{3}}$
Solution