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Question 26 Gravitation - Exercise

**(a) A cube of side 5 cm is immersed in water and then in a saturated salt solution. In which case will it experience a greater buoyant force. If each side of the cube is reduced to 4 cm and then immersed in water, what will be the effect on the buoyant force experienced by the cube as compared to the first case for water. Give a reason for each case.**

**(b) A ball weighing 4 kg of density 4000 kg m–3** **is completely immersed in water of density 103 kg m–3** **Find the force of buoyancy on it. (Given g = 10 m s–2)**

Answer:

(i) Buoyant force, F = Vpg

p = Density of water, V = volume of water displaced by the body

The volume and density of an object decide its Buoyancy. The cube will experience a greater buoyancy in a saturated solution. If the cube is reduced to 4 cm on each side, the volume of the cube becomes less as the buoyancy will be reduced as buoyant force is directly proportional to volume.

(ii) The magnitude of the buoyant force given by F = Vpg

where V = Volume of a body immersed in water or volume of water displaced, p = Density of liquid.[∴ Given, mass of a ball = 4 kg, density = 4000 kgm-3].

Hence Volume of solid = mass/density

= 4/4000

= 1/1000

Buoyancy F = Vpg

=1/1000x 1000×10

= 10N

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