A block of volume 3×10^5m^3 and density 2.5×10^5 kg/m^3 is suspended from a spring balance with 3/4 of it's volume immersed in a liquid of density 900kg/m^3. Determine the reading on spring balance
To determine the reading on the spring balance, we need to calculate the buoyant force acting on the block.
The buoyant force is equal to the weight of the liquid displaced by the block. The volume of the liquid displaced is given by 3/4 of the volume of the block.
Volume of liquid displaced = (3/4) * (3x10^5 m^3) = 2.25x10^5 m^3
The weight of the liquid displaced can be calculated using the equation:
Weight = density * volume * gravitational acceleration
Weight of liquid displaced = (900 kg/m^3) * (2.25x10^5 m^3) * (9.8 m/s^2)
= 1.7995x10^9 N
The buoyant force acting on the block is equal to the weight of the liquid displaced:
Buoyant force = 1.7995x10^9 N
The reading on the spring balance is equal to the weight of the block minus the buoyant force:
Reading = (density of block) * (volume of block) * (gravitational acceleration) - (buoyant force)
= (2.5x10^5 kg/m^3) * (3x10^5 m^3) * (9.8 m/s^2) - (1.7995x10^9 N)
= 7.35x10^17 N - 1.7995x10^9 N
= 7.35x10^17 N - 1.7995x10^9 N
≈ 7.35x10^17 N
Therefore, the reading on the spring balance is approximately 7.35x10^17 N.