a) $4.0 \times 10^3 \;N$

b) $2.5 \times 10^3 \;N$

c) $1.3 \times 10^3 \;N$

d) $3.0 \times 10^3 \;N$

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Difference in the pressure at the two positions is equal to the pressure due to liquid column of AB.

Pressure at larger position $P_1=\large\frac{F}{A_1}$

$\qquad= \large\frac{F}{\pi \bigg(\Large\frac{0.35}{2}\bigg)^2}$

Pressure at smaller position $P_2=\large\frac{20}{A_2}$

$\qquad= \large\frac{20 \times g}{\pi \bigg(\Large\frac{0.1}{2}\bigg)^2}$

$P_2-P_1=h \rho g$

$\large\frac{20 \times 9.8 }{\pi \times (5 \times 10^{-2})^2}- \large\frac{F}{\pi \times (17.5 \times 10^{-2})^2}$$= 1.5 \times 750 \times 9.8$

Solving we get,

$F= 1.3 \times 10^3\;N$

Hence c is the correct answer

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