Question

There is some water in the beaker placed on the pan of a spring balance. If we dip our finger in the water without touching the bottom of the beaker, then what is the change in the reading of spring balance?

Answer 1

Step 1: Archimedes Principle

Archimedes' principle states that an object immersed in a liquid receives an upward force equal to the weight of the displaced liquid. This is the first equilibrium state. The above force, called buoyancy, is assumed to be at the center of the underwater hull, called the center of buoyancy.

$F_b={\rho }_{liquid}gV$

where,
$F_b$= buoyant force
$\rho$= fluid density
$g$ = acceleration due to gravity
$V$= fluid volume

Step 2: Newton's third law of motion

Newton’s third law states that when two bodies interact, they apply forces to one another that are equal in magnitude and opposite in direction. The third law is also known as the law of action and reaction.

According to Newton's third law of motion, the finger exerts an equally downward and opposite force on the water, increasing the water by weight.

$F_{\mathrm{finger}}\left(\mathrm{downward}\right)=F_{\mathrm{water}}\left(\mathrm{upward}\right)$

When you immerse your finger in water, the water exerts an upward thrust on your finger (Archimedes principle). As a result, the weight of the water will increase.

Hence, there will be an increase in the spring balance reading.