Question 172 of 210

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 centre of mass (see figure). If the coefficient of friction is $\mu =0.4$ , the maximum possible value of $100\times \dfrac{b}{a}$ for a box not to topple before moving is ________

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Answer: 50

For no toppling
$F\left(\dfrac{a}{2}+b\right)\leq mg\dfrac{a}{2}$
$\mu \dfrac{a}{2}+\mu b\leq \dfrac{a}{2}$
$0.2a+0.4b\leq 0.5a$
$0.4b\leq 0.3a$
$b\leq \dfrac{3a}{2}$
$b\leq 0.75a$ (in limiting case)
But it is not possible as $b$ can maximum be equal to $0.5a$
$∴{\left(100\dfrac{b}{a}\right)}_{max}=50.00$