Question

A body of mass 70 kg, when completely immersed in water, displaces 20,000 cm3 of water. Find (i) the weight of body in water and (ii) the relative density of material of body.

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Answer

Mass of body = 70 kg

Volume of water displaced = 20,000 cm3 = 0.02 m3

(i) Mass of body immersed in water = mass of the water displaced

= volume of water displaced × density of water

= 0.02 × 1000

= 20 kg

Weight of the body = mg = 70 × g = 70 kgf

Weight of water displaced = mg = 20 × g = 20 kgf

Weight of body in water = weight of body in air – upthrust due to liquid

= 70 kgf – 20 kgf    [∵ upthrust is equal to the weight of water displaced]

= 50 kgf

(ii) Density = Mass\over Volume

= 70\over 0.02 = 3500 kg m-3

RD of body = 3500\over 1000 = 3.5

Therefore,

Relative density of body = 3.5

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