Consider the wall of a dam to be straight with height $H$ and length $L$. It holds a lake of water of height $h (h < H)$ on one side. Let the density of water be $\rho_{ w }$. Denote the torque about the axis along the bottom length of the wall by $\tau_1$. Denote also a similar torque due to the water up to height $h / 2$ and wall length $L / 2$ by $\tau_2$. Then $\tau_1 / \tau_2$ (ignore atmospheric pressure) is
Consider the wall of a dam to be straight with height $H$ and length $L$. It holds a lake of water of height $h (h < H)$ on one side. Let the density of water be $\rho_{ w }$. Denote the torque about the axis along the bottom length of the wall by $\tau_1$. Denote also a similar torque due to the water up to height $h / 2$ and wall length $L / 2$ by $\tau_2$. Then $\tau_1 / \tau_2$ (ignore atmospheric pressure) is
- [KVPY 2019]
- A
$2$
- B
$4$
- C
$8$
- D
$16$
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