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
A08
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#

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