Question

A cubical water tank is completely filled with water of mass m = 1000kg. The force exerted by the water on the side wall of the tank, is :

• A. (a) 1.062 x 10⁵N
• A. (b) 1.62 × 10⁵ N
• A. (c) 0.049 × 10⁵ N
• A. (d) None of these.

Answer 1

(a)

The cubical tank contains water of mass, M = 1000kg

⇒ volume of water V = $\frac{m}{\rho_{w}}$

$= \frac{1000kg}{1000kg/m^{3}}$= 1m³.

⇒ Volume of the tank = V = 1m³.

⇒ Side of the tank = b = 1m.

The pressure at A = $P_{A} = P_{atm}$.

The pressure at B = $P_{B} = P_{atm} + \rho gh = P_{atm} + \rho g\mathcal{l}$

⇒ The pressure at = $P_{C} = \frac{P_{A} + P_{B}}{2}$

= average pressure over the side wall

= $P_{atm} + \frac{\rho g\mathcal{l}}{2}$

The force exerted on the side wall is

F= $\left( P_{atm} + \frac{\rho gh}{2} \right)\left( \mathcal{l}^{2} \right)$

=$\left( 1.013 \times 10^{5} + \frac{10^{3} \times 9.8 \times 1}{2} \right)(1)^{2}N$ = (1.013 + 0.049)

⇒ × 10⁵ N

= 1.062 × 10⁵ N