Question

A solid of density 5000kg/$m^3$ weighs 0.5 kg f in air. It is completely immersed in water of density 1000kg/$m^3$. Calculate the apparent weight of the solid in water.

Answer 1

We know that the weight of a body is the attractive force exerted by the gravity on the body. Similarly, apparent weight is the vector sum of the weight of an accelerating body and the sum of all the negative forces acting on the body.

Complete step by step answer:
We know that apparent weight occurs when the force due to gravity on an object is unbalanced by its opposite normal force. This concept of apparent weight also leads to weightlessness of any body. Apparent weight is a property of objects that corresponds to how heavy an object is. The apparent weight of an object will differ from the weight of an object whenever the force of gravity acting on the object is not balanced by an equal but opposite normal force. We know the apparent weight is a property of objects relating to the heaviness of an object.
We can give the expression for apparent weight as:
$W = w - F$
Here, W is the apparent weight, w is the true weight and F is the upthrust. We will now substitute the required values.
$W = w - dgV$
Here, d is the density of water, V is the volume of solid and g is the acceleration due to gravity.
$\begin{array}{l} \Rightarrow W = w - dgV\\\ \Rightarrow W = w - dg\left( {\dfrac{{w/g}}{D}} \right) \end{array}$
Here, w/g is the mass of the solid and D is the density of the solid. We will now substitute the numerical values and we will get,
$\begin{array}{l} \Rightarrow W = w - w\left( {\dfrac{d}{D}} \right)\\\ \Rightarrow W = 0.5\;kgf - 0.5\;kgf\left( {\dfrac{{1000\;kg/{m^3}}}{{5000\;kg/{m^3}}}} \right)\\\ \Rightarrow W = 0.4\;kgf \end{array}$
Therefore, the apparent weight of the solid in water is 0.4 kgf.

Note: The normal force is equal and opposite to the force due to gravitation. Here, we are using three terms namely mass, weight and apparent weight, which might seem similar. But they are different and defined as follows:
1. Mass: it is a property of a body to resist the change in its motion.
2. Weight: it is the force of gravitation acting on a body.
3. Apparent weight: The difference in the weight and the forces acting on a body.