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Q.

In the figure, the cross-sectional area of the smaller tube is a and that of the larger tube is 2a. A block of mass m is kept in the smaller tube having the same base area a, as that of the tube. The difference between water levels of the two tubes is

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a

$\frac{P_{0}}{ρ g} + \frac{m}{a ρ}$

b

$\frac{m}{a ρ}$

c

$\frac{m}{2 a ρ}$

d

$\frac{P_{0}}{ρ g} + \frac{m}{2 a ρ}$

answer is C.

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Detailed Solution

Pressure at the bottom level of the block

$P = \frac{mg}{a} + P_{0}$

The pressure at the same level remains the same.

Hence, $\frac{mg}{a} + P_{0} = h ρ g + P_{0} \Rightarrow h = \frac{m}{a ρ}$

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In the figure, the cross-sectional area of the smaller tube is a and that of the larger tube is 2a. A block of mass m is kept in the smaller tube having the same base area a, as that of the tube. The difference between water levels of the two tubes is