A very large block of ice of the size of a volleyball court and of uniform thickness of $8 \,m$ is floating on water. A person standing near its edge wishes to fetch a bucketful of water using a rope. The smallest length of rope required for this is about ............... $m$
KVPY 2018, Medium
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(c)
Fraction of thickness of ice block out of water is
$x=1-\left(\frac{\rho_{\text {ice }}}{\rho_{\text {water }}}\right)=1-\frac{0.9}{1} \text { or } x=0.1$
So, minimum length of rope required $\approx$ thickness of ice $\times 0.1=8 \times 0.1=0.8 \,m$. Hence, nearest option is $0.9 \,m$.
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