Chapter 19, Problem 58A

A gravel barge, rectangular in shape, is 4 m wide and 10 m long. When loaded, it sinks 2 m in the water. Show that the weight of gravel in the barge is 800,000 N.

To determine

To show: Weight of gravel in the barge is 800,000 N.

Explanation of Solution

Given:

The dimensions of gravel barge are 4 m wide and 10 m long and it sinks 2 m deep.

Formula Used:

The buoyancy force is given as,

  $F_{\text{buoyancy}}=\rho Vg$

Where, $\rho$ is density, $V$ is volume of liquid displaced and $g$ is gravitational acceleration.

Calculation:

According to Archimedes principle,

  $w_{\text{gravel}}=w_{\text{water}\text{displaced}}=\rho Vg$

As, ${\rho }_{\text{waterr}}=1000{\text{kg/m}}^3$ and $g=10\text{N/kg}$

So, on substituting the values weight of gravel is

  $\begin{array}{l}{w}_{\text{gravel}}=\left(1000{\text{g/cm}}^3\right)\times \left(2\text{m}\times 4\text{m}\times 10\text{m}\right)\times 10\text{N/kg}\\ =\text{800,000 N}\end{array}$

Conclusion:

Hence it is proved that weight of gravel in the barge is 800,000 N