Q134 / 170 · Manipal (MET) 2021 · Physics

To what height should a rectangular cylinder having square base of length 10 cm be filled, so that the total force on the bottom is equal to that on the sides ?

  • Correct answer
    A
    5 cm
  • B
    10 cm
  • C
    20 cm
  • D
    6.67 cm

Solution

If $h$ is the height of liquid column in cylinder and $I$ is the length of each side of base. Then $\begin{aligned} & F_B=(h \rho g)(I \times l)=h \rho g l^2 \\ & F_S=\left(\frac{h \rho g}{2}\right)(4 I \times h)=2 h^2 \rho g l\end{aligned}$ $\therefore \quad h \rho g l^2=2 h^2 \rho g l$ or $h=\frac{1}{2}=\frac{10}{2}=5 \mathrm{~cm}$

Hence, the correct answer is option: 'A'.

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