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Physics · MECHANICAL PROPERTIES OF FLUIDS
हिन्दीIn a faulty Torricelli mercury barometer, some air is trapped above the mercury column. When the true atmospheric pressure is \( 76\text{ cm of Hg} \), the barometer tube has a length of \( 80\text{ cm} \) above the trough level, but the mercury column stands at \( 70\text{ cm} \). If the tube is pushed further down into the reservoir until the length above the mercury level is \( 60\text{ cm} \), what will be the new height of the mercury column? (Assume constant temperature)
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Correct answer · Option B
\( 50\text{ cm} \)
Explanation
Initially, trapped air length \( L_1 = 80 - 70 = 10\text{ cm} \), pressure \( P_1 = 76 - 70 = 6\text{ cm Hg} \). In the second state, \( L_2 = 60 - h \), \( P_2 = 76 - h \). By Boyle's law: \( P_1 L_1 = P_2 L_2 \implies 6 \times 10 = (76 - h)(60 - h) \implies h^2 - 136h + 4500 = 0 \implies (h - 50)(h - 86) = 0 \). Since \( h < 60\text{ cm} \), \( h = 50\text{ cm} \).
