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  4. A glass tumbler having inner depth of 17.5 cm is kept on a table. A student starts pouring water (μ=4 / 3) into it while looking at the surface of water from the above. When he feels that the tumbler is half filled, he stops pouring water. Up to what height, the tumbler is actually filled?

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Q. A glass tumbler having inner depth of $17.5\, cm$ is kept on a table. A student starts pouring water $(\mu=4 / 3)$ into it while looking at the surface of water from the above. When he feels that the tumbler is half filled, he stops pouring water. Up to what height, the tumbler is actually filled?

JEE MainJEE Main 2021Mechanical Properties of Fluids

Solution:

image
Height of water observed by observer
$=\frac{ H }{\mu_{ w }}=\frac{ H }{(4 / 3)}=\frac{3 H }{4}$
Height of air observed by observer $=17.5- H$ According to question,
both height observed by observer is same.
$\frac{3 H }{4}=17.5- H$
$\Rightarrow H =10 \,cm$