A block of mass 5kg hanging at the end of spring scale is totally submerged in a beaker of water. The beaker is large enough to avoid overflow of water. If the density of the block is 2500kg/m^3,then what is the reading of the scale?

1 Answer
Jun 2, 2018

Volume of block V="Mass"/"Density"=5/2500=0.002\ m^3
From Archimedes' principle we know that a body when immersed in a fluid, fully or partially, experiences an the upward buoyant force equal to the weight of the fluid displaced. As the body is fully submerged in water, volume of water displaced =V.

Upward buoyant force

F_uarr="weight of volume V of water"=rhoVg
where rho=1000\ kgm^-3 is density of water and g=9.8\ ms^-2 acceleration due to gravity

Downward force is weight of block

"Weight"="mass of block"xxg

Reading on the spring scale

R="weight"-F_uarr
=>R=5xx9.8-1000xx0.002xx9.8
=>R=9.8(5-2)
=>R=29.4\ N