A block of material of volume 2 X 1O-5m3 and density 2.5 x 10-3 kgm-3 is suspended from a spring balance with half volume of the block immersed in water. Wh...

A block of material of volume 2 X 1O^-5m³ and density 2.5 x 10^-3 kgm^-3 is suspended from a spring balance with half volume of the block immersed in water. What is the reading of the spring balance? (Density of water =1.0x10³ kg m^-3 g = 10 ms^-2).

Answer Details

The weight of the block is given by the formula: Weight = Volume x Density x g where g is the acceleration due to gravity. Therefore, the weight of the block is: Weight = (2 x 10^-5 m^3) x (2.5 x 10^-3 kg/m^3) x (10 m/s^2) = 5 x 10^-4 N When the block is half-immersed in water, the upthrust on the block is equal to the weight of the water displaced. The volume of water displaced is half the volume of the block, so the weight of the water displaced is: Weight of water = Volume of water x Density of water x g = (1 x 10^-5 m^3) x (1.0 x 10^3 kg/m^3) x (10 m/s^2) = 0.1 N The reading on the spring balance is equal to the weight of the block minus the weight of the water displaced, so: Reading = Weight - Weight of water = (5 x 10^-4 N) - (0.1 N) = 0.4 N Therefore, the reading on the spring balance is 0.40N.