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A square gate of size 1 \mathrm{~m} \times 1 \mathrm{~m} is hinged at its mid-point. A fluid of density  ' \rho ' fills space to the left of the gate. The force F required to hold the gate stationary is:

Option: 1

\mathrm{\frac{\rho g}{3}}


Option: 2

\mathrm{\frac{\rho g}{2}}


Option: 3

\mathrm{\frac{\rho g}{6}}


Option: 4

\mathrm{\text { none of these }}


Answers (1)

best_answer

\mathrm{\begin{aligned} & F(1 / 2)=\int_0^{1 / 2} \rho g(1 / 2+x) x d x-\int_0^{1 / 2} \rho g(1 / 2-x) x d x \\ & F=\frac{1}{6} \rho g \end{aligned}}

Posted by

Irshad Anwar

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