A level controller is shown in the figure. It consists of a thin ci...

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A level controller is shown in the figure. It consists of a thin circular plug of diameter \( 10 \mathrm{~cm} \) and a cylindrical float of diameter \( 20 \mathrm{~cm} \) tied together with a light rigid rod of length \( 10 \mathrm{~cm} \). The plug fits in snugly in a drain hole at the bottom of the tank which opens into atmosphere. As water fills up and the level reaches height \( h \), the plug opens. Find \( h \). Determine the level of water in the tank when the plug closes - again. The float has a mass \( 3 \mathrm{~kg} \) and the plug may be assumed as massless.
\( \mathrm{P} \)
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